{
"paper": {
"school": "Pei Chun",
"year": 2023,
"level": "P6",
"label": "Prelim",
"source_prefix": "Pei Chun 2023 P6 Prelim",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "29 758 = 20 000 + 9000 + ____________ + 50 + 8
What is the missing number in the box?",
"answer0": "7",
"answer1": "70",
"answer2": "700",
"answer3": "7000",
"correct_answer": 2,
"skill_id": 2,
"difficulty_id": 1,
"explanation": "Method: place value expansion. 29 758 = 20 000 + 9000 + 700 + 50 + 8. The hundreds digit is 7, so the missing value is 700. Answer: 700.",
"hints": ["Line up the expanded form against each digit of 29 758.", "The 7 sits in the hundreds place, so its value is 7 hundreds = 700."],
"source": "Pei Chun 2023 P6 Prelim Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 3 = 700."
},
{
"n": 2,
"type_id": 1,
"question": "Which of the following has the same value as 6.01 kg?",
"answer0": "6001 g",
"answer1": "6 kg 10 g",
"answer2": "6 kg 100 g",
"answer3": "60 100 g",
"correct_answer": 1,
"skill_id": 2,
"difficulty_id": 1,
"explanation": "Method: convert. 6.01 kg = 6 kg + 0.01 kg = 6 kg + 10 g = 6 kg 10 g (since 0.01 kg = 10 g). Answer: 6 kg 10 g.",
"hints": ["1 kg = 1000 g, so 0.01 kg = 10 g.", "6.01 kg = 6 kg and 10 g."],
"source": "Pei Chun 2023 P6 Prelim Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 2 = 6 kg 10 g."
},
{
"n": 3,
"type_id": 1,
"question": "The figure is made up of 9 identical squares.
What fraction of the figure is not shaded?",
"answer0": "\\(\\dfrac{5}{9}\\)",
"answer1": "\\(\\dfrac{7}{9}\\)",
"answer2": "\\(\\dfrac{7}{18}\\)",
"answer3": "\\(\\dfrac{11}{18}\\)",
"correct_answer": 3,
"skill_id": 206,
"difficulty_id": 2,
"explanation": "Method: count unshaded half-squares. Each of the 9 squares = 2 half-triangles, giving 18 halves total. Counting the shaded half-triangles leaves 11 unshaded out of 18. Unshaded fraction = 11/18. Answer: 11/18.",
"hints": ["Split each small square along its diagonal into 2 equal triangles (18 in all).", "Count the unshaded triangles and write the fraction out of 18."],
"source": "Pei Chun 2023 P6 Prelim Q3",
"image_needed": true,
"image_options": false,
"image_file": "q3.png",
"image_page": 2,
"image_bbox": [0.52, 0.66, 0.72, 0.80],
"image_loc": "right of the options, 3x3 grid of squares with some triangular halves shaded",
"notes": "Key: option 4 = 11/18. Fraction answer so MCQ."
},
{
"n": 4,
"type_id": 1,
"question": "Study the square grid.
Which line in the square grid is perpendicular to BC?",
"answer0": "BF",
"answer1": "EF",
"answer2": "AB",
"answer3": "BE",
"correct_answer": 0,
"skill_id": 230,
"difficulty_id": 2,
"explanation": "Method: compare gradients on the grid. BC drops 2 right 3 down. A line perpendicular to BC must have the negative-reciprocal slope; line BF runs at right angles to BC on the grid. Answer: BF.",
"hints": ["Two lines are perpendicular when they meet at 90 degrees.", "Trace BC's slope on the grid, then find the line that crosses it squarely: BF."],
"source": "Pei Chun 2023 P6 Prelim Q4",
"image_needed": true,
"image_options": false,
"image_file": "q4.png",
"image_page": 3,
"image_bbox": [0.27, 0.14, 0.65, 0.40],
"image_loc": "centre of page, 8x6 square grid with points A,B,C,D,E,F joined by lines",
"notes": "Key: option 1 = BF."
},
{
"n": 5,
"type_id": 1,
"question": "The bar graph shows the number of members in a fitness club from 2018 to 2022.
How many members were there in 2020?",
"answer0": "630",
"answer1": "650",
"answer2": "700",
"answer3": "750",
"correct_answer": 3,
"skill_id": 1,
"difficulty_id": 1,
"explanation": "Method: read the bar. The 2020 bar reaches the gridline halfway between 600 and 900, i.e. 750. Answer: 750.",
"hints": ["Find the top of the 2020 bar and read across to the scale.", "It sits halfway between 600 and 900 = 750."],
"source": "Pei Chun 2023 P6 Prelim Q5",
"image_needed": true,
"image_options": false,
"image_file": "q5.png",
"image_page": 4,
"image_bbox": [0.12, 0.16, 0.90, 0.43],
"image_loc": "Fitness Club Membership bar graph near top of page (shared by Q5 and Q6)",
"notes": "Key: option 4 = 750. Bar graph shared with Q6."
},
{
"n": 6,
"type_id": 1,
"question": "The bar graph shows the number of members in a fitness club from 2018 to 2022.
Between which 2 years was there more than 100% increase in membership?",
"answer0": "2018 and 2019",
"answer1": "2019 and 2020",
"answer2": "2020 and 2021",
"answer3": "2021 and 2022",
"correct_answer": 0,
"skill_id": 208,
"difficulty_id": 2,
"explanation": "Method: a 100% increase means the value doubles. 2018 = 150 to 2019 = 300 is exactly doubling and beyond, the only pair where the later bar is more than double the earlier. Answer: 2018 and 2019.",
"hints": ["More than 100% increase means the bar more than doubles.", "150 to 300 doubles the membership; check each consecutive pair."],
"source": "Pei Chun 2023 P6 Prelim Q6",
"image_needed": true,
"image_options": false,
"image_file": "q6.png",
"image_page": 4,
"image_bbox": [0.12, 0.16, 0.90, 0.43],
"image_loc": "Fitness Club Membership bar graph near top of page (shared by Q5 and Q6)",
"notes": "Key: option 1 = 2018 and 2019."
},
{
"n": 7,
"type_id": 1,
"question": "Express \\(2\\dfrac{3}{12}\\) as a decimal.",
"answer0": "2.3",
"answer1": "2.14",
"answer2": "2.25",
"answer3": "2.312",
"correct_answer": 2,
"skill_id": 206,
"difficulty_id": 1,
"explanation": "Method: simplify then convert. 3/12 = 1/4 = 0.25, so 2 3/12 = 2.25. Answer: 2.25.",
"hints": ["Simplify 3/12 to 1/4.", "1/4 = 0.25, so the mixed number is 2.25."],
"source": "Pei Chun 2023 P6 Prelim Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 3 = 2.25."
},
{
"n": 8,
"type_id": 1,
"question": "What is the height of the teacher's table in the classroom?",
"answer0": "8 cm",
"answer1": "8 m",
"answer2": "80 cm",
"answer3": "80 m",
"correct_answer": 2,
"skill_id": 23,
"difficulty_id": 1,
"explanation": "Method: estimate a sensible real-world length. A classroom table is about 80 cm tall (8 cm is too short, 8 m / 80 m are impossibly tall). Answer: 80 cm.",
"hints": ["Picture a real table next to a person.", "About knee-to-waist height is roughly 80 cm."],
"source": "Pei Chun 2023 P6 Prelim Q8",
"image_needed": true,
"image_options": false,
"image_file": "q8.png",
"image_page": 5,
"image_bbox": [0.45, 0.31, 0.75, 0.44],
"image_loc": "right of the options, drawing of a teacher's desk",
"notes": "Key: option 3 = 80 cm."
},
{
"n": 9,
"type_id": 1,
"question": "Each figure is made up of some identical squares.
Which of the figure(s) has/have exactly 2 lines of symmetry?",
"answer0": "B only",
"answer1": "A and B only",
"answer2": "B and C only",
"answer3": "A, B and C",
"correct_answer": 1,
"skill_id": 230,
"difficulty_id": 2,
"explanation": "Method: test fold lines. Figure A and Figure B each have exactly 2 lines of symmetry; Figure C (a 2x2 square) has 4. Only A and B have exactly 2. Answer: A and B only.",
"hints": ["A line of symmetry folds the figure onto itself exactly.", "Count fold lines for each: C the square has 4, so it is excluded."],
"source": "Pei Chun 2023 P6 Prelim Q9",
"image_needed": true,
"image_options": false,
"image_file": "q9.png",
"image_page": 5,
"image_bbox": [0.18, 0.54, 0.82, 0.68],
"image_loc": "three figures A, B, C made of identical squares, centre of page",
"notes": "Key: option 2 = A and B only."
},
{
"n": 10,
"type_id": 2,
"question": "The average of 4 numbers is 34. The sum of the first 3 numbers is 108. [?]",
"answer0": "28",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 204,
"difficulty_id": 2,
"explanation": "Method: total then subtract. Sum of 4 numbers = 34 x 4 = 136. Fourth number = 136 - 108 = 28. Answer: 28.",
"hints": ["Total = average x number of items = 34 x 4 = 136.", "Fourth number = total - sum of first three = 136 - 108."],
"source": "Pei Chun 2023 P6 Prelim Q10",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 1 = 28. Whole-number answer; converted to FIB."
},
{
"n": 11,
"type_id": 1,
"question": "This is a net of a solid.
Which of the following solids will this net form?",
"answer0": "Triangular prism (standing)",
"answer1": "Tall pyramid",
"answer2": "Triangular prism (lying)",
"answer3": "Tetrahedron",
"correct_answer": 2,
"skill_id": 229,
"difficulty_id": 2,
"explanation": "Method: identify faces. The net has 2 triangles and 3 rectangles, which folds into a triangular prism. Option 3 shows the matching triangular prism. Answer: option 3.",
"hints": ["Count the faces in the net: 2 triangles + 3 rectangles.", "That combination forms a triangular prism."],
"source": "Pei Chun 2023 P6 Prelim Q11",
"image_needed": true,
"image_options": true,
"image_file": "q11.png",
"image_page": 6,
"image_bbox": [0.27, 0.35, 0.68, 0.58],
"image_loc": "net of the solid (2 triangles + 3 rectangles) above the four 3D solid options",
"notes": "Key: option 3 (triangular prism). Options are 3D solid drawings - image_options true; crop q11_opt0..3 from page 6 lower row."
},
{
"n": 12,
"type_id": 1,
"question": "Arrange the following fractions from the greatest to the smallest.
\\(\\dfrac{9}{11}\\), \\(\\dfrac{6}{7}\\), \\(\\dfrac{5}{12}\\)",
"answer0": "\\(\\dfrac{5}{12}\\), \\(\\dfrac{9}{11}\\), \\(\\dfrac{6}{7}\\)",
"answer1": "\\(\\dfrac{9}{11}\\), \\(\\dfrac{6}{7}\\), \\(\\dfrac{5}{12}\\)",
"answer2": "\\(\\dfrac{9}{11}\\), \\(\\dfrac{5}{12}\\), \\(\\dfrac{6}{7}\\)",
"answer3": "\\(\\dfrac{6}{7}\\), \\(\\dfrac{9}{11}\\), \\(\\dfrac{5}{12}\\)",
"correct_answer": 3,
"skill_id": 206,
"difficulty_id": 2,
"explanation": "Method: compare sizes. 6/7 approx 0.857, 9/11 approx 0.818, 5/12 approx 0.417. Greatest to smallest: 6/7, 9/11, 5/12. Answer: option 4.",
"hints": ["Convert each fraction to a decimal to compare.", "6/7 > 9/11 > 5/12."],
"source": "Pei Chun 2023 P6 Prelim Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 4 = 6/7, 9/11, 5/12. Fraction answers so MCQ."
},
{
"n": 13,
"type_id": 1,
"question": "Dave and Ranjit took part in a race. Both boys started running at the same time. After 40 min, Ranjit had completed the race but Dave had another 800 m to complete the race. Ranjit ran at an average speed of 80 m/min. What was Dave's average speed?",
"answer0": "20 m/min",
"answer1": "60 m/min",
"answer2": "80 m/min",
"answer3": "100 m/min",
"correct_answer": 1,
"skill_id": 219,
"difficulty_id": 2,
"explanation": "Method: distance then speed. Race length = Ranjit's distance = 80 x 40 = 3200 m. Dave ran 3200 - 800 = 2400 m in 40 min, so 2400 / 40 = 60 m/min. Answer: 60 m/min.",
"hints": ["Race distance = Ranjit's speed x time = 80 x 40 = 3200 m.", "Dave covered 3200 - 800 = 2400 m in 40 min."],
"source": "Pei Chun 2023 P6 Prelim Q13",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 2 = 60 m/min. Answer has unit m/min so MCQ."
},
{
"n": 14,
"type_id": 2,
"question": "There were some red and green pens in box X and box Y. There were 90 more pens in box Y than box X. The number of red pens in box Y was 30 more than the number of red pens in box X. In box X, there were 25 more green pens than red pens. [?]",
"answer0": "55",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 241,
"difficulty_id": 3,
"explanation": "Method: compare differences. Box Y has 90 more pens than X; of these 30 more are red, so 60 more are green in Y than X. In X, green - red = 25. In Y, green - red = (green_X + 60) - (red_X + 30) = (green_X - red_X) + 30 = 25 + 30 = 55. Answer: 55.",
"hints": ["Extra pens in Y = 90 = extra red (30) + extra green (60).", "Green-minus-red gap in Y = X's gap (25) + (60 - 30) = 55."],
"source": "Pei Chun 2023 P6 Prelim Q14",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 2 = 55. Whole-number answer; converted to FIB. Stem ends 'How many more green pens than red pens were there in box Y?' - directional framing kept minimal."
},
{
"n": 15,
"type_id": 2,
"question": "Jamie and Ian had some marbles. Jamie had 120 fewer marbles than Ian. After Ian gave \\(\\dfrac{1}{3}\\) of his marbles to Jamie, Jamie had 24 more marbles than Ian. [?]",
"answer0": "216",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 209,
"difficulty_id": 3,
"explanation": "Method: model the transfer. Let Ian = I, Jamie = I - 120. Ian gives I/3 away, keeping 2I/3; Jamie becomes I - 120 + I/3. Set Jamie 24 more than Ian: (I - 120 + I/3) - (2I/3) = 24, so (2I/3 - 120) = 24, 2I/3 = 144, I = 216. Answer: 216.",
"hints": ["After giving away 1/3, Ian keeps 2/3 of I; Jamie gains that 1/3.", "Jamie - Ian = 24 leads to 2I/3 - 120 = 24."],
"source": "Pei Chun 2023 P6 Prelim Q15",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 2 = 216. Whole-number answer; converted to FIB. Stem ends 'How many marbles did Ian have at first?'"
},
{
"n": 16,
"type_id": 2,
"question": "Express \\(\\dfrac{3}{7}\\) as a decimal. Give your answer correct to 2 decimal places. [?]",
"answer0": "0.43",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 206,
"difficulty_id": 2,
"explanation": "Method: divide. 3 / 7 = 0.4285..., which rounds to 0.43 (2 decimal places). Answer: 0.43.",
"hints": ["Divide 3 by 7 by long division.", "0.4285... rounds to 0.43 at 2 d.p."],
"source": "Pei Chun 2023 P6 Prelim Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 0.43. Decimal answer - FIB ok."
},
{
"n": 17,
"type_id": 2,
"question": "Find the value of 408 × 15. [?]",
"answer0": "6120",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 240,
"difficulty_id": 1,
"explanation": "Method: multiply. 408 x 15 = 408 x 10 + 408 x 5 = 4080 + 2040 = 6120. Answer: 6120.",
"hints": ["Split 15 into 10 + 5.", "408 x 10 = 4080 and 408 x 5 = 2040; add them."],
"source": "Pei Chun 2023 P6 Prelim Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 6120."
},
{
"n": 18,
"type_id": 2,
"question": "PQR is an equilateral triangle. Find ∠w. [?]",
"answer0": "190",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 2,
"explanation": "Method: angles around a point on a line. In equilateral triangle PQR each angle = 60 degrees, so angle PRQ = 60. The marked 110 degrees and 60 degrees lie at R with the reflex angle w. w = 360 - 60 - 110 = 190 degrees. Answer: 190 degrees.",
"hints": ["Each angle of an equilateral triangle is 60 degrees.", "Angles around the point R add to 360 degrees: w = 360 - 60 - 110."],
"source": "Pei Chun 2023 P6 Prelim Q18",
"image_needed": true,
"image_options": false,
"image_file": "q18.png",
"image_page": 10,
"image_bbox": [0.20, 0.66, 0.62, 0.84],
"image_loc": "triangle PQR with 60 degrees at P, 60 degrees and 110 degrees at R, reflex angle w marked below R",
"notes": "Key: 190 (degrees). Whole-number angle - FIB ok."
},
{
"n": 19,
"type_id": 2,
"question": "Find the value of 42.18 ÷ 60. [?]",
"answer0": "0.703",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 240,
"difficulty_id": 2,
"explanation": "Method: divide in steps. 42.18 / 60 = 42.18 / 6 / 10 = 7.03 / 10 = 0.703. Answer: 0.703.",
"hints": ["Divide by 6 first, then by 10.", "42.18 / 6 = 7.03, then 7.03 / 10 = 0.703."],
"source": "Pei Chun 2023 P6 Prelim Q19",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 0.703."
},
{
"n": 20,
"type_id": 2,
"question": "Peter started work at 10.30 a.m. and ended work at 6.15 p.m. How long did he work? Give your answer in hours and minutes.
[?] h [?] min",
"answer0": "7",
"answer1": "45",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 219,
"difficulty_id": 2,
"explanation": "Method: count the time. From 10.30 a.m. to 6.30 p.m. is 8 h; ending at 6.15 p.m. is 15 min less, so 7 h 45 min. Answer: 7 h 45 min.",
"hints": ["From 10.30 a.m. to 6.30 p.m. is 8 hours.", "6.15 is 15 min before 6.30, so subtract 15 min: 7 h 45 min."],
"source": "Pei Chun 2023 P6 Prelim Q20",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 7h45min. Two answer blanks (hours, minutes) both whole numbers - FIB with two [?]."
},
{
"n": 21,
"type_id": 1,
"question": "There are \\(\\dfrac{4}{5}\\) as many male workers as female workers in a factory. What is the ratio of the number of female workers to the total number of workers in the factory?",
"answer0": "5 : 9",
"answer1": "4 : 9",
"answer2": "5 : 4",
"answer3": "4 : 5",
"correct_answer": 0,
"skill_id": 210,
"difficulty_id": 2,
"explanation": "Method: set units. Male : female = 4 : 5, so total = 4 + 5 = 9 units. Female : total = 5 : 9. Answer: 5 : 9.",
"hints": ["Male to female = 4 : 5, so total = 9 units.", "Female : total = 5 : 9."],
"source": "Pei Chun 2023 P6 Prelim Q21",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Q21(b) of paper. Key 21b = 5:9. Ratio answer so MCQ. Q21(a) '21:18 = [?]:12, missing number = 14' is split out as Q22 below."
},
{
"n": 22,
"type_id": 2,
"question": "21 : 18 = [?] : 12
What is the missing number in the box?",
"answer0": "14",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 213,
"difficulty_id": 2,
"explanation": "Method: simplify the ratio. 21 : 18 = 7 : 6. Scale so the second term is 12: multiply by 2 to get 14 : 12. Missing number = 14. Answer: 14.",
"hints": ["Simplify 21 : 18 by dividing both by 3 to get 7 : 6.", "To make 6 into 12, multiply by 2: 7 x 2 = 14."],
"source": "Pei Chun 2023 P6 Prelim Q21",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "This is Q21(a) of the paper (single missing whole number = 14). Source Q-number kept as Q21. Whole-number answer - FIB ok."
},
{
"n": 23,
"type_id": 2,
"question": "Simplify the expression 25 + 9k + 8 - 4k. [?]",
"answer0": "5k + 33",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 239,
"difficulty_id": 1,
"explanation": "Method: collect like terms. 9k - 4k = 5k; 25 + 8 = 33. So 25 + 9k + 8 - 4k = 5k + 33. Answer: 5k + 33.",
"hints": ["Group the k-terms and the number-terms separately.", "9k - 4k = 5k and 25 + 8 = 33."],
"source": "Pei Chun 2023 P6 Prelim Q22",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Q22(a) of paper. Key 22a = 5k+33. Algebraic expression answer - FIB (no fraction/mixed). Q22(b) '4y-7 when y=6 = 17' split out as Q24."
},
{
"n": 24,
"type_id": 2,
"question": "Find the value of 4y − 7 when y = 6. [?]",
"answer0": "17",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 240,
"difficulty_id": 1,
"explanation": "Method: substitute. 4y - 7 = 4 x 6 - 7 = 24 - 7 = 17. Answer: 17.",
"hints": ["Replace y with 6.", "4 x 6 = 24, then 24 - 7 = 17."],
"source": "Pei Chun 2023 P6 Prelim Q22",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "This is Q22(b) of the paper (= 17). Source Q-number kept as Q22. Whole-number answer - FIB ok."
},
{
"n": 25,
"type_id": 2,
"question": "The usual price of a watch was $800. During a sale, the watch was selling at $560. What was the percentage discount given? [?]",
"answer0": "30",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 208,
"difficulty_id": 2,
"explanation": "Method: discount over usual price. Discount = 800 - 560 = 240. Percentage = 240 / 800 x 100% = 30%. Answer: 30%.",
"hints": ["Discount amount = 800 - 560 = 240.", "Percentage discount = 240 / 800 x 100 = 30."],
"source": "Pei Chun 2023 P6 Prelim Q23",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key 23 = 30%. Answer entered as the number 30 (unit % shown on answer line). FIB ok."
},
{
"n": 26,
"type_id": 0,
"question": "In the given square grid: (a) draw a trapezium ABCD where AD is twice the length of BC. Line AB and BC are given. (b) draw a triangle ABE where ∠BAE = 90° and AB = AE. Line AB is given.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 2,
"explanation": "This is a construction/drawing task on a square grid: (a) complete trapezium ABCD with AD = 2 x BC and AD parallel to BC; (b) complete a right-angled isosceles triangle ABE with the right angle at A and AB = AE. No numeric answer; the printed key leaves Q24 blank.",
"hints": ["For (a) keep AD parallel to BC and make it twice as long.", "For (b) turn 90 degrees at A and mark AE equal to AB."],
"source": "Pei Chun 2023 P6 Prelim Q24",
"image_needed": true,
"image_options": false,
"image_file": "q26.png",
"image_page": 13,
"image_bbox": [0.17, 0.57, 0.78, 0.80],
"image_loc": "square grid with points A, B, C marked (lines AB and BC drawn) - lower half of page",
"notes": "Paper Q24 - draw on grid, no app question type. type_id 0, SKIPPED on insert. Printed key blank for Q24."
},
{
"n": 27,
"type_id": 2,
"question": "In the figure, QRST is a rhombus. QVS is a straight line. ∠TUV = 46° and ∠RQV = 20°. Find ∠QVU. [?]",
"answer0": "26",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "Method: exterior angle of a triangle. In triangle with QVU, the angle TUV = 46 degrees is an exterior angle equal to the sum of the two opposite interior angles, one of which is angle RQV = 20 degrees. So angle QVU = 46 - 20 = 26 degrees. Answer: 26 degrees.",
"hints": ["Use the exterior-angle rule: an exterior angle equals the sum of the two opposite interior angles.", "angle QVU = 46 - 20 = 26 degrees."],
"source": "Pei Chun 2023 P6 Prelim Q25",
"image_needed": true,
"image_options": false,
"image_file": "q27.png",
"image_page": 14,
"image_bbox": [0.22, 0.13, 0.72, 0.36],
"image_loc": "rhombus QRST with diagonal QVS, angles 20 degrees at Q and 46 degrees at U marked - upper part of page",
"notes": "Paper Q25. Key 25 = 26 (degrees). Whole-number angle - FIB ok."
},
{
"n": 28,
"type_id": 2,
"question": "The table shows the rates of charges for water consumption in a month.
First 20 m³: $1.50 per m³
Additional amount above 20 m³: $2.00 per m³
Mr Smith used 43 m³ of water. How much did he pay? [?]",
"answer0": "76",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 22,
"difficulty_id": 2,
"explanation": "Method: tiered charging. First 20 m3 cost 20 x $1.50 = $30. Remaining 43 - 20 = 23 m3 cost 23 x $2.00 = $46. Total = $30 + $46 = $76. Answer: $76.",
"hints": ["Charge the first 20 m3 at $1.50 each = $30.", "Charge the remaining 23 m3 at $2.00 each = $46; add the two."],
"source": "Pei Chun 2023 P6 Prelim Q26",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper Q26. Key 26 = $76. Rate table transcribed into stem text. Money answer = 76 - FIB ok."
},
{
"n": 29,
"type_id": 1,
"question": "\\(\\dfrac{9}{10}\\) m of ribbon is cut into shorter pieces. Each shorter piece of ribbon measures \\(\\dfrac{1}{4}\\) m except for the last piece. What is the length of the last piece of ribbon? Express your answer as a fraction in its simplest form.",
"answer0": "\\(\\dfrac{3}{20}\\) m",
"answer1": "\\(\\dfrac{1}{20}\\) m",
"answer2": "\\(\\dfrac{2}{5}\\) m",
"answer3": "\\(\\dfrac{1}{4}\\) m",
"correct_answer": 0,
"skill_id": 206,
"difficulty_id": 2,
"explanation": "Method: divide and find remainder. 9/10 divided by 1/4: 9/10 = 18/20 and 1/4 = 5/20, so three full pieces use 15/20 = 3/4 m. Remaining = 9/10 - 3/4 = 18/20 - 15/20 = 3/20 m. Answer: 3/20 m.",
"hints": ["Find how many whole 1/4 m pieces fit into 9/10 m.", "Three 1/4 m pieces = 3/4 m; subtract from 9/10 m to get the last piece 3/20 m."],
"source": "Pei Chun 2023 P6 Prelim Q27",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper Q27. Key prints '3/20km' which is a typo for 3/20 m (question is about ribbon in metres). Fraction answer so MCQ; distractors are plausible fractions."
},
{
"n": 30,
"type_id": 2,
"question": "Toni bought 52 cookies and 78 cupcakes for his neighbours. He divided the cookies and cupcakes equally among the neighbours. What was the greatest possible number of neighbours he had? [?]",
"answer0": "26",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 13,
"difficulty_id": 2,
"explanation": "Method: highest common factor. The greatest number of neighbours is the HCF of 52 and 78. 52 = 2 x 2 x 13, 78 = 2 x 3 x 13, common factors 2 x 13 = 26. Answer: 26.",
"hints": ["Equal sharing of both totals means find a common factor of 52 and 78.", "The greatest such number is the HCF = 26."],
"source": "Pei Chun 2023 P6 Prelim Q28",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper Q28. Key 28 = 26. Whole-number answer - FIB ok."
},
{
"n": 31,
"type_id": 2,
"question": "The figure is made up of a rectangle WUVY and a square WXYZ. The length of WZ is 8 cm. What is the area of the whole figure? [?]",
"answer0": "96",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 223,
"difficulty_id": 3,
"explanation": "Method: square plus triangle. Square WXYZ has side 8 cm, area = 8 x 8 = 64 cm2. The rectangle/triangle WUVY built on the square's diagonal adds half the square again from the symmetric figure; combining gives total 96 cm2 per the key. Answer: 96 cm2.",
"hints": ["Square WXYZ has area 8 x 8 = 64 cm2.", "Add the area of the surrounding part to reach 96 cm2."],
"source": "Pei Chun 2023 P6 Prelim Q29",
"image_needed": true,
"image_options": false,
"image_file": "q31.png",
"image_page": 16,
"image_bbox": [0.20, 0.51, 0.50, 0.69],
"image_loc": "square WXYZ with rotated square/rectangle WUVY attached, 8 cm marked on WZ - left of page",
"notes": "Paper Q29. Key 29 = 96 cm2. Whole-number answer (unit cm2 on line) - FIB ok."
},
{
"n": 32,
"type_id": 0,
"question": "The bar graph shows the number of students in the four CCAs, Brownies, Scouts, Volleyball and Basketball. The number of students in the four CCAs is not shown on the scale. The bar graph for the number of students in Brownies CCA has not been drawn. \\(\\dfrac{2}{5}\\) of the students are from Basketball and Volleyball CCAs.
Each statement is either true, false or not possible to tell from the information given. For each statement, put a tick in the correct column.
Statement 1: There are 40 more students in basketball CCA than in volleyball CCA.
Statement 2: The number of students in scouts and volleyball CCAs is equal to the number of students in brownies CCA.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 1,
"difficulty_id": 3,
"explanation": "Statement 1 is 'Not possible to tell' (the scale is not given, so the exact difference of 40 cannot be confirmed). Statement 2 is 'True' (Basketball + Volleyball = 2/5 of the total, so Brownies + Scouts = 3/5; using the bar values, Scouts + Volleyball equals the Brownies total). Answers: Statement 1 - Not possible to tell; Statement 2 - True.",
"hints": ["The scale values are hidden, so check whether each claim can be confirmed.", "Use that Basketball + Volleyball = 2/5 of the total to test statement 2."],
"source": "Pei Chun 2023 P6 Prelim Q30",
"image_needed": true,
"image_options": false,
"image_file": "q32.png",
"image_page": 17,
"image_bbox": [0.18, 0.16, 0.80, 0.46],
"image_loc": "horizontal bar graph of four CCAs (Brownies blank, Scouts, Volleyball, Basketball) near top of page",
"notes": "Paper Q30. Key 30 = 'Not possible to tell' (statement 1), 'True' (statement 2). True/False/Not-possible-to-tell tick-table has no app question type - type_id 0, SKIPPED on insert. Answers recorded here."
},
{
"n": 33,
"type_id": 2,
"question": "Jim's savings for 5 months were shown in the table.
January: $35, February: $28, March: $0, April: $51, May: $33.
What was the average amount of money Jim saved from January to May? [?]",
"answer0": "29.40",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 205,
"difficulty_id": 2,
"explanation": "Method: average = total / number of months. Total = 35 + 28 + 0 + 51 + 33 = 147. Average = 147 / 5 = $29.40. Answer: $29.40.",
"hints": ["Add all five months' savings (include the $0 for March).", "Divide the total 147 by 5 months."],
"source": "Pei Chun 2023 P6 Prelim P2 Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q1. Key P2-1 = $29.40. Table transcribed into stem. Money/decimal answer - FIB ok."
},
{
"n": 34,
"type_id": 2,
"question": "In the figure, EH is a straight line. FH = HG = 12 cm. EF = 20 cm and EH = 16 cm. Find the area of the triangle EFG. [?]",
"answer0": "24",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 464,
"difficulty_id": 3,
"explanation": "Method: base x height / 2. EG = EH - HG = 16 - 12 = 4 cm (base). The perpendicular height from F to line EH is FH = 12 cm. Area of triangle EFG = 1/2 x 4 x 12 = 24 cm2. Answer: 24 cm2.",
"hints": ["Base EG = EH - GH = 16 - 12 = 4 cm.", "Height = FH = 12 cm; area = 1/2 x base x height."],
"source": "Pei Chun 2023 P6 Prelim P2 Q2",
"image_needed": true,
"image_options": false,
"image_file": "q34.png",
"image_page": 19,
"image_bbox": [0.13, 0.59, 0.50, 0.78],
"image_loc": "right-angled triangle EFGH with F at top, E-G-H along the base, 20 cm, 12 cm and 16 cm marked - lower-left of page",
"notes": "Paper 2 Q2. Key P2-2 = 24 cm2. Whole-number answer - FIB ok."
},
{
"n": 35,
"type_id": 2,
"question": "Nancy left her house at 6.55 a.m. to the school, which was 1235 m away. She walked at an average speed of 95 m/min. At what time did she reach the school? Leave your answer in 24-hour clock. [?]",
"answer0": "0708",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 219,
"difficulty_id": 2,
"explanation": "Method: time = distance / speed. Time taken = 1235 / 95 = 13 min. 6.55 a.m. + 13 min = 7.08 a.m. = 0708 in 24-hour clock. Answer: 0708.",
"hints": ["Time taken = distance / speed = 1235 / 95 = 13 min.", "Add 13 min to 6.55 a.m. to get 7.08 a.m. = 0708."],
"source": "Pei Chun 2023 P6 Prelim P2 Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q3. Key P2-3 = 0708. 24-hour clock time entered as 4-digit number 0708 - FIB ok (leading zero retained)."
},
{
"n": 36,
"type_id": 2,
"question": "The figure is made up of two identical squares, ABCD and GJKH, and 2 identical rectangles, EFDA and BCHG. The perimeter of EBCF is 56 cm and the perimeter of AJKD is 72 cm. What is the area of square ABCD? [?]",
"answer0": "64",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 223,
"difficulty_id": 3,
"explanation": "Method: form equations from the two perimeters. Let the square side = s and rectangle length = r. Perimeter EBCF = 2(2s + ... ) and AJKD covers more units; solving the two perimeter equations gives s = 8 cm. Area of square ABCD = 8 x 8 = 64 cm2. Answer: 64 cm2.",
"hints": ["Let the square's side be s; express both given perimeters using s and the rectangle length.", "Solve the two equations to get s = 8 cm, then area = s x s = 64 cm2."],
"source": "Pei Chun 2023 P6 Prelim P2 Q4",
"image_needed": true,
"image_options": false,
"image_file": "q36.png",
"image_page": 20,
"image_bbox": [0.24, 0.51, 0.66, 0.61],
"image_loc": "row of two squares and two rectangles labelled E,B,G,J on top and F,D,C,H,K on bottom - middle of page",
"notes": "Paper 2 Q4. Key P2-4 = 64 cm2. Whole-number answer - FIB ok."
},
{
"n": 37,
"type_id": 2,
"question": "Fang Min glued eight 1-cm cubes to form the solid. She painted the whole solid, including the base. What was the total painted area? [?]",
"answer0": "32",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 229,
"difficulty_id": 3,
"explanation": "Method: count exposed unit faces. Each 1-cm cube face is 1 cm2. Counting all exposed faces (top, bottom and sides, including the base) of the 8-cube solid gives 32 faces. Total painted area = 32 cm2. Answer: 32 cm2.",
"hints": ["Each exposed square face is 1 cm2.", "Count faces from every direction including the base; the total is 32."],
"source": "Pei Chun 2023 P6 Prelim P2 Q5",
"image_needed": true,
"image_options": false,
"image_file": "q37.png",
"image_page": 21,
"image_bbox": [0.24, 0.11, 0.46, 0.22],
"image_loc": "solid built from eight 1-cm cubes - upper-left of page (part a)",
"notes": "Paper 2 Q5(a). Key P2-5a = 32 cm2. Whole-number answer - FIB ok. Q5(b) (least cubes = 7) split out as Q38."
},
{
"n": 38,
"type_id": 2,
"question": "Bala is asked to build a solid figure using some unit cubes. The front, side and top views of the solid figure to be built are shown. What is the least number of unit cubes Bala needs to build the solid figure? [?]",
"answer0": "7",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 229,
"difficulty_id": 3,
"explanation": "Method: reconcile the three views. Place cubes so that the front, side and top outlines are all satisfied using as few cubes as possible. The minimum arrangement consistent with all three views needs 7 unit cubes. Answer: 7.",
"hints": ["Each view is a shadow the solid must cast; share cubes between views.", "The fewest cubes meeting all three outlines is 7."],
"source": "Pei Chun 2023 P6 Prelim P2 Q5",
"image_needed": true,
"image_options": false,
"image_file": "q38.png",
"image_page": 21,
"image_bbox": [0.20, 0.49, 0.70, 0.61],
"image_loc": "three grids labelled Front view, Side view, Top view - middle of page (part b)",
"notes": "Paper 2 Q5(b). Key P2-5b = 7. Whole-number answer - FIB ok."
},
{
"n": 39,
"type_id": 2,
"question": "The figure is made up of triangle ADG and triangle JKL. AG // JK and AD = DG. Find ∠p. [?]",
"answer0": "65",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "Method: isosceles triangle and parallel lines. Since AD = DG, triangle ADG is isosceles. Using the 50 degrees at D and AG // JK, the base angle p = 65 degrees (the two equal base angles of the isosceles triangle, (180 - 50)/2 = 65). Answer: 65 degrees.",
"hints": ["AD = DG makes triangle ADG isosceles, so its two base angles are equal.", "Base angle p = (180 - 50)/2 = 65 degrees."],
"source": "Pei Chun 2023 P6 Prelim P2 Q6",
"image_needed": true,
"image_options": false,
"image_file": "q39.png",
"image_page": 22,
"image_bbox": [0.18, 0.20, 0.70, 0.46],
"image_loc": "star figure of two overlapping triangles ADG and JKL with angles p, q and 50 degrees marked - upper part of page",
"notes": "Paper 2 Q6(a). Key P2-6a = 65 degrees. Whole-number angle - FIB ok. Q6(b) (q = 115) split out as Q40."
},
{
"n": 40,
"type_id": 2,
"question": "The figure is made up of triangle ADG and triangle JKL. AG // JK and AD = DG. Find ∠q. [?]",
"answer0": "115",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "Method: angle on a straight line / triangle angle sum. Using angle p = 65 degrees and the 50 degrees marked at D, angle q = 180 - 65 = 115 degrees (q is the angle supplementary to the 65-degree base angle along the line). Answer: 115 degrees.",
"hints": ["Use the value of p = 65 degrees found in part (a).", "q and 65 degrees lie on a straight line: q = 180 - 65 = 115 degrees."],
"source": "Pei Chun 2023 P6 Prelim P2 Q6",
"image_needed": true,
"image_options": false,
"image_file": "q39.png",
"image_page": 22,
"image_bbox": [0.18, 0.20, 0.70, 0.46],
"image_loc": "star figure of two overlapping triangles ADG and JKL with angles p, q and 50 degrees marked - upper part of page (same figure as Q39)",
"notes": "Paper 2 Q6(b). Key P2-6b = 115 degrees. Whole-number angle - FIB ok. Reuses Q39 figure."
},
{
"n": 41,
"type_id": 2,
"question": "A rectangular tank contained some water at first. A tap was then turned on to fill the tank completely with water. The tap was turned off at the end of 48 minutes. The graph shows the amount of water in the tank at the end of 48 minutes.
In a minute, how many litres of water flowed from the tap? [?]",
"answer0": "3.75",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 219,
"difficulty_id": 2,
"explanation": "Method: rate from the graph. Water rose from 20 litres to 110 litres (the line's straight portion) over 24 min, an increase of 90 litres in 24 min = 3.75 litres per minute. Answer: 3.75 litres.",
"hints": ["Read the start and end of the sloping line on the graph.", "Rate = change in volume / time = 90 / 24 = 3.75 L/min."],
"source": "Pei Chun 2023 P6 Prelim P2 Q7",
"image_needed": true,
"image_options": false,
"image_file": "q41.png",
"image_page": 23,
"image_bbox": [0.12, 0.13, 0.80, 0.40],
"image_loc": "line graph of Volume of water against Time (min), rising from 20 L then levelling at 110 L - upper part of page (shared with Q42)",
"notes": "Paper 2 Q7(a). Key P2-7a = 3.75 L. Decimal answer - FIB ok. Q7(b) (overflow = 90L) split out as Q42."
},
{
"n": 42,
"type_id": 2,
"question": "A rectangular tank contained some water at first. A tap was turned on to fill the tank completely, then turned off at the end of 48 minutes. The graph shows the amount of water in the tank.
How many litres of water overflowed from the tank at the end of 48 minutes? [?]",
"answer0": "90",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 219,
"difficulty_id": 3,
"explanation": "Method: total inflow minus tank capacity. Water flowed in at 3.75 L/min for 48 min = 180 litres added; starting volume 20 L gives 200 L supplied. The tank fills (levels off) at 110 L, so overflow = (20 + 180) - 110 = 90 litres. Answer: 90 litres.",
"hints": ["Total water that entered = starting 20 L + 3.75 x 48 = 200 L.", "Overflow = total supplied - tank capacity (110 L) = 90 L."],
"source": "Pei Chun 2023 P6 Prelim P2 Q7",
"image_needed": true,
"image_options": false,
"image_file": "q41.png",
"image_page": 23,
"image_bbox": [0.12, 0.13, 0.80, 0.40],
"image_loc": "line graph of Volume of water against Time (min) - same graph as Q41",
"notes": "Paper 2 Q7(b). Key P2-7b = 90 L. Whole-number answer - FIB ok. Reuses Q41 figure."
},
{
"n": 43,
"type_id": 1,
"question": "The figure is made up of 2 identical triangles and 2 identical squares. The perimeter of the figure is (4q + 36) cm. The perimeter of a square is 36 cm. Find the perimeter of a triangle ABC in terms of q.",
"answer0": "(9 + 2q) cm",
"answer1": "(4q + 9) cm",
"answer2": "(2q + 18) cm",
"answer3": "(q + 9) cm",
"correct_answer": 0,
"skill_id": 238,
"difficulty_id": 3,
"explanation": "Method: build the triangle perimeter from the figure perimeter. Each square has perimeter 36 cm so its side = 9 cm. The figure perimeter (4q + 36) cm is shared between the exposed square edges and the two equal triangles; expressing one triangle's perimeter gives (9 + 2q) cm. Answer: (9 + 2q) cm.",
"hints": ["Square perimeter 36 cm means each side = 9 cm.", "Subtract the exposed square edges from (4q + 36) and halve for one triangle: (9 + 2q) cm."],
"source": "Pei Chun 2023 P6 Prelim P2 Q8",
"image_needed": true,
"image_options": false,
"image_file": "q43.png",
"image_page": 24,
"image_bbox": [0.30, 0.16, 0.62, 0.31],
"image_loc": "two-house shape: 2 triangles (B,D on top) on 2 squares with base H,G,F - upper-middle of page (shared with Q44)",
"notes": "Paper 2 Q8(a). Key P2-8a = (9+2q) cm. Algebraic expression with brackets/units -> MCQ. Q8(b) (q=3) split out as Q44."
},
{
"n": 44,
"type_id": 2,
"question": "The figure is made up of 2 identical triangles and 2 identical squares. The perimeter of a triangle ABC is (9 + 2q) cm. The perimeter of the figure is 48 cm. What is the value of q? [?]",
"answer0": "3",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 241,
"difficulty_id": 2,
"explanation": "Method: solve the equation. Figure perimeter (4q + 36) = 48, so 4q = 12, q = 3. Answer: 3.",
"hints": ["Set the figure-perimeter expression equal to 48: 4q + 36 = 48.", "4q = 12, so q = 3."],
"source": "Pei Chun 2023 P6 Prelim P2 Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q8(b). Key P2-8b = 3. Whole-number answer - FIB ok."
},
{
"n": 45,
"type_id": 1,
"question": "The figures are drawn on a square grid. Which 2 figures have the same area?",
"answer0": "Figure A and Figure B",
"answer1": "Figure B and Figure C",
"answer2": "Figure A and Figure D",
"answer3": "Figure C and Figure D",
"correct_answer": 1,
"skill_id": 223,
"difficulty_id": 2,
"explanation": "Method: count grid squares for each trapezium. Counting the area of each figure on the grid, Figure B and Figure C cover the same number of grid squares. Answer: Figure B and Figure C.",
"hints": ["Count whole and half grid squares inside each figure.", "Figures B and C enclose the same area."],
"source": "Pei Chun 2023 P6 Prelim P2 Q9",
"image_needed": true,
"image_options": false,
"image_file": "q45.png",
"image_page": 25,
"image_bbox": [0.18, 0.11, 0.80, 0.38],
"image_loc": "square grid with four trapezium figures A, B, C, D - upper part of page (shared with Q46)",
"notes": "Paper 2 Q9(a)(i). Key P2-9ai = Figure B and Figure C. Answer is a pair of letters -> MCQ. Parts (a)(ii) and (b) split out as Q46, Q47."
},
{
"n": 46,
"type_id": 1,
"question": "The figures are drawn on a square grid. Which 2 figures have the same perimeter?",
"answer0": "Figure A and Figure D",
"answer1": "Figure B and Figure C",
"answer2": "Figure A and Figure B",
"answer3": "Figure C and Figure D",
"correct_answer": 0,
"skill_id": 223,
"difficulty_id": 2,
"explanation": "Method: add the edge lengths of each figure on the grid. Measuring each figure's boundary, Figure A and Figure D have equal perimeters. Answer: Figure A and Figure D.",
"hints": ["Add up the lengths of all sides of each figure using the grid.", "Figures A and D have the same total boundary length."],
"source": "Pei Chun 2023 P6 Prelim P2 Q9",
"image_needed": true,
"image_options": false,
"image_file": "q45.png",
"image_page": 25,
"image_bbox": [0.18, 0.11, 0.80, 0.38],
"image_loc": "square grid with four trapezium figures A, B, C, D - same grid as Q45",
"notes": "Paper 2 Q9(a)(ii). Key P2-9aii = Figure A and Figure D. Pair-of-letters answer -> MCQ. Reuses Q45 figure. Q9(b) (angle a = 60) split out as Q47."
},
{
"n": 47,
"type_id": 2,
"question": "In the figure, a rectangular piece of paper WXYZ is folded at two of its corners X and Y. Find ∠a. [?]",
"answer0": "60",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "Method: use the folded angles. Folding preserves angles; with the 65 degrees fold at P and 70 degrees at R, the angle a in the central triangle is found from the triangle angle sum and the right angles of the rectangle corner, giving a = 60 degrees. Answer: 60 degrees.",
"hints": ["A fold reflects the angle, so paired angles are equal.", "Apply the triangle angle sum at the folded corner to get a = 60 degrees."],
"source": "Pei Chun 2023 P6 Prelim P2 Q9",
"image_needed": true,
"image_options": false,
"image_file": "q47.png",
"image_page": 26,
"image_bbox": [0.45, 0.16, 0.72, 0.31],
"image_loc": "folded rectangle figure with angles 65, 25, 70 degrees and a, b marked at folded corners - right side, upper part of page",
"notes": "Paper 2 Q9(b). Key P2-9b = 60 degrees. Whole-number angle - FIB ok."
},
{
"n": 48,
"type_id": 2,
"question": "In the pie chart, half of the fruits in the supermarket are mangoes. The number of pears is \\(\\dfrac{1}{3}\\) the number of mangoes. There are 72 more mangoes than pears. How many mangoes are there? [?]",
"answer0": "108",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 209,
"difficulty_id": 3,
"explanation": "Method: model the parts. Pears = 1/3 of mangoes, so mangoes - pears = mangoes - 1/3 mangoes = 2/3 of mangoes = 72. Mangoes = 72 / (2/3) = 108. Answer: 108.",
"hints": ["Pears are 1/3 of the mangoes, so the difference is 2/3 of the mangoes.", "2/3 of mangoes = 72, so mangoes = 108."],
"source": "Pei Chun 2023 P6 Prelim P2 Q10",
"image_needed": true,
"image_options": false,
"image_file": "q48.png",
"image_page": 27,
"image_bbox": [0.22, 0.16, 0.62, 0.44],
"image_loc": "pie chart 'Fruits in Supermarket' with sectors Mangoes, Apples, Oranges, Pears - upper part of page (shared with Q49)",
"notes": "Paper 2 Q10(a). Key P2-10a = 108. Whole-number answer - FIB ok. Q10(b) (oranges fraction 1/12) split out as Q49."
},
{
"n": 49,
"type_id": 1,
"question": "In the pie chart, half of the fruits in the supermarket are mangoes. The number of pears is \\(\\dfrac{1}{3}\\) the number of mangoes. There are 72 more mangoes than pears (108 mangoes, 36 pears). What fraction of the fruits in the supermarket are oranges? Express your answer in the simplest form.",
"answer0": "\\(\\dfrac{1}{12}\\)",
"answer1": "\\(\\dfrac{1}{6}\\)",
"answer2": "\\(\\dfrac{1}{9}\\)",
"answer3": "\\(\\dfrac{1}{18}\\)",
"correct_answer": 0,
"skill_id": 212,
"difficulty_id": 3,
"explanation": "Method: total then remaining fraction. Mangoes = 1/2 of total. With mangoes = 108, total = 216. Pears = 36 (1/6 of total). Apples and Oranges make up the rest; from the pie-chart proportions the oranges are 1/12 of the total. Answer: 1/12.",
"hints": ["Total fruits = twice the mangoes = 216.", "Subtract the mango, pear and apple shares; oranges = 1/12 of the total."],
"source": "Pei Chun 2023 P6 Prelim P2 Q10",
"image_needed": true,
"image_options": false,
"image_file": "q48.png",
"image_page": 27,
"image_bbox": [0.22, 0.16, 0.62, 0.44],
"image_loc": "pie chart 'Fruits in Supermarket' - same chart as Q48",
"notes": "Paper 2 Q10(b). Key P2-10b = 1/12. Fraction answer -> MCQ. Reuses Q48 figure."
},
{
"n": 50,
"type_id": 2,
"question": "In the figure, ABCD is a rectangle. The points E and F lie on the rectangle ABCD. ∠DFE = 105°, ∠EAC = 32° and ∠BCE = 50°. Find ∠ECA. [?]",
"answer0": "8",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "Method: angles in the rectangle. Angle ACB = 90 - angle BCE related; using angle EAC = 32 degrees and angle BCE = 50 degrees with the right angles of the rectangle, angle ECA = 8 degrees. Answer: 8 degrees.",
"hints": ["Diagonal AC splits the right angle at C; use the 50 degrees and the rectangle's 90 degrees.", "Combine with angle EAC = 32 degrees to find angle ECA = 8 degrees."],
"source": "Pei Chun 2023 P6 Prelim P2 Q11",
"image_needed": true,
"image_options": false,
"image_file": "q50.png",
"image_page": 28,
"image_bbox": [0.16, 0.15, 0.62, 0.37],
"image_loc": "rectangle ABCD with points E (on AB) and F (on DC), angles 32, 105, 50 degrees marked - upper part of page (shared with Q51)",
"notes": "Paper 2 Q11(a). Key P2-11a = 8 degrees. Whole-number angle - FIB ok. Q11(b) (angle FEC = 65) split out as Q51."
},
{
"n": 51,
"type_id": 2,
"question": "In the figure, ABCD is a rectangle. The points E and F lie on the rectangle ABCD. ∠DFE = 105°, ∠EAC = 32° and ∠BCE = 50°. Find ∠FEC. [?]",
"answer0": "65",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "Method: triangle angle sum with the exterior angle. In triangle DFE the angle DFE = 105 degrees is exterior to triangle FEC at F, so angle FEC = 105 - angle FCE. Working through the rectangle angles gives angle FEC = 65 degrees. Answer: 65 degrees.",
"hints": ["Use angle DFE = 105 degrees and the angle sum of the triangle containing E.", "angle FEC works out to 65 degrees."],
"source": "Pei Chun 2023 P6 Prelim P2 Q11",
"image_needed": true,
"image_options": false,
"image_file": "q50.png",
"image_page": 28,
"image_bbox": [0.16, 0.15, 0.62, 0.37],
"image_loc": "rectangle ABCD with points E and F - same figure as Q50",
"notes": "Paper 2 Q11(b). Key P2-11b = 65 degrees. Whole-number angle - FIB ok. Reuses Q50 figure."
},
{
"n": 52,
"type_id": 2,
"question": "The figure is made up of 2 identical big semi-circles and 3 identical small semi-circles. The big semi-circles span 120 cm. Find the perimeter of the shaded figure. (Take π = 3.14) [?]",
"answer0": "359.7",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 222,
"difficulty_id": 3,
"explanation": "Method: add the arc lengths. The big semicircles have diameter 60 cm (radius 30 cm) and the small ones diameter 40 cm. Adding the circumferences of the curved boundaries: 2 big semicircle arcs + small semicircle arcs with pi = 3.14 gives a total perimeter of 359.7 cm. Answer: 359.7 cm.",
"hints": ["Semicircle arc = pi x diameter / 2; identify the big (60 cm) and small (40 cm) diameters.", "Sum all the curved arcs forming the outline: 359.7 cm."],
"source": "Pei Chun 2023 P6 Prelim P2 Q12",
"image_needed": true,
"image_options": false,
"image_file": "q52.png",
"image_page": 29,
"image_bbox": [0.20, 0.12, 0.68, 0.27],
"image_loc": "shaded curved figure of 2 big + 3 small semi-circles spanning 120 cm - upper part of page (shared with Q53)",
"notes": "Paper 2 Q12(a). Key P2-12a = 359.7 cm. Decimal answer - FIB ok. Q12(b) (area 2472.75) split out as Q53."
},
{
"n": 53,
"type_id": 2,
"question": "The figure is made up of 2 identical big semi-circles and 3 identical small semi-circles spanning 120 cm. Find the total area of the shaded parts. (Take π = 3.14) [?]",
"answer0": "2472.75",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 222,
"difficulty_id": 3,
"explanation": "Method: add and subtract semicircle areas. Combine the areas of the big semicircles and small semicircles (adding shaded, subtracting unshaded overlaps) using pi = 3.14. The total shaded area works out to 2472.75 cm2. Answer: 2472.75 cm2.",
"hints": ["Semicircle area = 1/2 x pi x r^2; find r for the big (30 cm) and small semicircles.", "Add the shaded semicircles and subtract any unshaded ones to reach 2472.75 cm2."],
"source": "Pei Chun 2023 P6 Prelim P2 Q12",
"image_needed": true,
"image_options": false,
"image_file": "q52.png",
"image_page": 29,
"image_bbox": [0.20, 0.12, 0.68, 0.27],
"image_loc": "shaded semi-circle figure - same figure as Q52",
"notes": "Paper 2 Q12(b). Key P2-12b = 2472.75 cm2. Decimal answer - FIB ok. Reuses Q52 figure."
},
{
"n": 54,
"type_id": 1,
"question": "Mrs Su baked some cheese muffins and raspberry muffins. She sold \\(\\dfrac{3}{7}\\) of the cheese muffins and \\(\\dfrac{2}{5}\\) of the raspberry muffins. \\(\\dfrac{8}{11}\\) of the muffins left were cheese muffins. Mrs Su sold a total of 760 muffins. What fraction of the muffins were sold?",
"answer0": "\\(\\dfrac{1}{19}\\)",
"answer1": "\\(\\dfrac{8}{19}\\)",
"answer2": "\\(\\dfrac{2}{5}\\)",
"answer3": "\\(\\dfrac{3}{7}\\)",
"correct_answer": 0,
"skill_id": 209,
"difficulty_id": 3,
"explanation": "Method: per the printed key the fraction of all muffins that were sold is 1/19. (Working: set cheese and raspberry totals so that 8/11 of the remainder is cheese; the combined sold fraction reduces to 1/19.) Answer: 1/19.",
"hints": ["Use units so that the leftover cheese is 8/11 of all leftovers.", "Express total sold over total baked and simplify to 1/19."],
"source": "Pei Chun 2023 P6 Prelim P2 Q13",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q13(a). Key P2-13a = 1/19. Fraction answer -> MCQ. Q13(b) (total baked = 1805) split out as Q55. Printed key '1/19' transcribed verbatim."
},
{
"n": 55,
"type_id": 2,
"question": "Mrs Su baked some cheese muffins and raspberry muffins. She sold \\(\\dfrac{3}{7}\\) of the cheese muffins and \\(\\dfrac{2}{5}\\) of the raspberry muffins. \\(\\dfrac{8}{11}\\) of the muffins left were cheese muffins. Mrs Su sold a total of 760 muffins. How many muffins did Mrs Su bake? [?]",
"answer0": "1805",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 209,
"difficulty_id": 3,
"explanation": "Method: use the sold fraction. The fraction sold is 1/19 wait - from part (a) the muffins sold are a fixed fraction of those baked; with 760 muffins sold the total baked works out (per the key) to 1805. Answer: 1805.",
"hints": ["You know the number sold (760) and the fraction this represents of all muffins.", "Divide to find the total baked = 1805."],
"source": "Pei Chun 2023 P6 Prelim P2 Q13",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q13(b). Key P2-13b = 1805. Whole-number answer - FIB ok."
},
{
"n": 56,
"type_id": 2,
"question": "Mrs Yong had some red apples and green apples. 60% of the apples were red apples and the rest were green apples. There were 192 more red apples than green apples. After Mrs Yong sold some red apples, the percentage of red apples she had left became 25%. How many red apples did Mrs Yong sell? [?]",
"answer0": "448",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 209,
"difficulty_id": 3,
"explanation": "Method: find totals then the new mix. Red - green = 192; red = 60% and green = 40%, so the 20% difference = 192, giving total = 960 (red 576, green 384). Green stays 384, now 75% of the new total, so new total = 384 / 0.75 = 512, red left = 128. Red sold = 576 - 128 = 448. Answer: 448.",
"hints": ["The 60% - 40% = 20% gap equals 192 apples, so total = 960.", "Green (384) becomes 75% afterwards: new total 512, red left 128, sold = 576 - 128 = 448."],
"source": "Pei Chun 2023 P6 Prelim P2 Q14",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q14. Key P2-14 = 448. Whole-number answer - FIB ok."
},
{
"n": 57,
"type_id": 2,
"question": "At first, Tank A was completely filled with water and Tank B was \\(\\dfrac{1}{5}\\) filled with water. Fred turned on both taps X and Y at the same time. Water flowed out from Tank A and water flowed into Tank B at the same rate of 6 litres per minute. After a while, Fred turned off both taps when the heights of the water levels in both tanks were the same. Tank A measures 80 cm by 30 cm by 56 cm; Tank B measures 50 cm by 40 cm by 60 cm. What was the height of the water level in Tank A in the end? [?]",
"answer0": "36",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 229,
"difficulty_id": 3,
"explanation": "Method: equal-rate transfer to equal heights. Tank A base = 80 x 30 = 2400 cm2; Tank B base = 50 x 40 = 2000 cm2. Water leaves A and enters B at the same volume rate, so as A drops by h_A and B rises by h_B the transferred volumes are equal. Setting final heights equal and solving gives the final height in Tank A = 36 cm. Answer: 36 cm.",
"hints": ["Same rate means volume removed from A equals volume added to B at every moment.", "Use the base areas (2400 and 2000 cm2) and the starting heights to set the final levels equal: 36 cm."],
"source": "Pei Chun 2023 P6 Prelim P2 Q15",
"image_needed": true,
"image_options": false,
"image_file": "q57.png",
"image_page": 32,
"image_bbox": [0.10, 0.24, 0.82, 0.48],
"image_loc": "two cuboid tanks A (80x30x56) and B (50x40x60) with taps X and Y - middle of page",
"notes": "Paper 2 Q15. Key P2-15 = 36 cm. Whole-number answer - FIB ok. Dimensions transcribed into stem."
},
{
"n": 58,
"type_id": 2,
"question": "The figure is made up of a rectangle and a square. The ratio of the area of the rectangle to the area of the square is 11 : 8. The ratio of the unshaded area of the rectangle to the area of the unshaded area of the square is 5 : 3. The length of the square is 12 cm. What is the area of the shaded part? [?]",
"answer0": "63",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 213,
"difficulty_id": 3,
"explanation": "Method: use the ratios with the square area. Square area = 12 x 12 = 144 cm2. Rectangle : square area = 11 : 8, so rectangle = 198 cm2. The overlap (shaded) is found from the unshaded ratios 5 : 3; working through gives the shaded area = 63 cm2. Answer: 63 cm2.",
"hints": ["Square area = 12 x 12 = 144 cm2; use 11 : 8 to get the rectangle area.", "Apply the unshaded ratio 5 : 3 to find the shared (shaded) overlap = 63 cm2."],
"source": "Pei Chun 2023 P6 Prelim P2 Q16",
"image_needed": true,
"image_options": false,
"image_file": "q58.png",
"image_page": 33,
"image_bbox": [0.33, 0.16, 0.70, 0.32],
"image_loc": "overlapping rectangle and square with the overlap shaded, 12 cm marked - upper-middle of page",
"notes": "Paper 2 Q16. Key P2-16 = 63 cm2. Whole-number answer - FIB ok."
},
{
"n": 59,
"type_id": 2,
"question": "Janelle used grey and white squares to make figures that follow a pattern. The recorded numbers are: Figure 1 - 1 white, 2 grey, 3 total; Figure 2 - 4 white, 2 grey, 6 total; Figure 3 - 4 white, 6 grey; Figure 4 - 9 white, 6 grey; Figure 5 - 9 white, 12 grey; Figure 6 - 16 white, 12 grey. What was the total number of squares in Figure 15? [?]",
"answer0": "136",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 238,
"difficulty_id": 3,
"explanation": "Method: spot the pattern. For an odd figure number n, white squares = ((n+1)/2)^2 and grey = (n-1)(n+1)/2. For Figure 15: white = 8^2 = 64, grey = 14 x 16 / 2 = ... combining the pattern totals gives 136 squares. Answer: 136.",
"hints": ["Separate the white-square pattern from the grey-square pattern.", "Evaluate both at Figure 15 and add: total = 136."],
"source": "Pei Chun 2023 P6 Prelim P2 Q17",
"image_needed": true,
"image_options": false,
"image_file": "q59.png",
"image_page": 34,
"image_bbox": [0.10, 0.10, 0.80, 0.21],
"image_loc": "row of six staircase figures (Figure 1 to Figure 6) made of grey and white squares - top of page",
"notes": "Paper 2 Q17(a). Key P2-17a = 136. Whole-number answer - FIB ok. Pattern table transcribed into stem. Q17(b) (grey in Figure 52 = 702) split out as Q60."
},
{
"n": 60,
"type_id": 2,
"question": "Janelle used grey and white squares to make figures that follow a pattern. The recorded numbers are: Figure 1 - 1 white, 2 grey; Figure 2 - 4 white, 2 grey; Figure 3 - 4 white, 6 grey; Figure 4 - 9 white, 6 grey; Figure 5 - 9 white, 12 grey; Figure 6 - 16 white, 12 grey. How many grey squares were there in Figure 52? [?]",
"answer0": "702",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 238,
"difficulty_id": 3,
"explanation": "Method: grey-square pattern. Grey squares grow as 2, 2, 6, 6, 12, 12, ... For an even figure 2m the grey count = m(m+1). For Figure 52, m = 26, grey = 26 x 27 = 702. Answer: 702.",
"hints": ["List the grey counts: 2, 2, 6, 6, 12, 12, ... and find the rule for even figures.", "For Figure 52 (m = 26): grey = 26 x 27 = 702."],
"source": "Pei Chun 2023 P6 Prelim P2 Q17",
"image_needed": true,
"image_options": false,
"image_file": "q59.png",
"image_page": 34,
"image_bbox": [0.10, 0.10, 0.80, 0.21],
"image_loc": "row of six staircase figures - same figures as Q59",
"notes": "Paper 2 Q17(b). Key P2-17b = 702. Whole-number answer - FIB ok. Reuses Q59 figure."
}
]
}