{
"paper": {
"school": "Maris Stella",
"year": 2023,
"level": "P6",
"label": "Prelim",
"source_prefix": "Maris Stella 2023 P6 Prelim",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "Which of the following is seventy-five thousand and thirty in numerals?",
"answer0": "7530",
"answer1": "75 030",
"answer2": "75 300",
"answer3": "750 030",
"correct_answer": 1,
"skill_id": 149,
"difficulty_id": 1,
"explanation": "Seventy-five thousand = 75 000; and thirty = 30. So the number is 75 000 + 30 = 75 030. Answer: 75 030.",
"hints": ["Write seventy-five thousand as 75 000.", "Add thirty (30) to it."],
"source": "Maris Stella 2023 P6 Prelim Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key = option (2) = 75 030."
},
{
"n": 2,
"type_id": 1,
"question": "The diagram shows a tablet used in a lesson in the classroom. Which of the following could be the mass of the tablet?",
"answer0": "8 g",
"answer1": "8 kg",
"answer2": "80 kg",
"answer3": "800 g",
"correct_answer": 3,
"skill_id": 184,
"difficulty_id": 1,
"explanation": "A tablet device has a sensible real-world mass. 8 g is far too light, 8 kg and 80 kg are far too heavy. A reasonable mass is 800 g. Answer: 800 g.",
"hints": ["Compare each value to everyday objects.", "A tablet weighs less than 1 kg but much more than a few grams."],
"source": "Maris Stella 2023 P6 Prelim Q2",
"image_needed": true,
"image_options": false,
"image_file": "q2.png",
"image_page": 3,
"image_bbox": [0.66, 0.36, 0.92, 0.55],
"image_loc": "right side of page, grey tablet rectangle beside the options",
"notes": "Key = option (4) = 800 g. Estimation of reasonable mass."
},
{
"n": 3,
"type_id": 1,
"question": "Arrange these fractions from the smallest to the largest.
\\(\\dfrac{4}{5}\\) \\(\\dfrac{3}{7}\\) \\(\\dfrac{2}{3}\\)",
"answer0": "\\(\\dfrac{2}{3}\\), \\(\\dfrac{3}{7}\\), \\(\\dfrac{4}{5}\\)",
"answer1": "\\(\\dfrac{3}{7}\\), \\(\\dfrac{4}{5}\\), \\(\\dfrac{2}{3}\\)",
"answer2": "\\(\\dfrac{3}{7}\\), \\(\\dfrac{2}{3}\\), \\(\\dfrac{4}{5}\\)",
"answer3": "\\(\\dfrac{4}{5}\\), \\(\\dfrac{2}{3}\\), \\(\\dfrac{3}{7}\\)",
"correct_answer": 2,
"skill_id": 79,
"difficulty_id": 2,
"explanation": "Convert to a common denominator 105: \\(\\dfrac{4}{5}=\\dfrac{84}{105}\\), \\(\\dfrac{3}{7}=\\dfrac{45}{105}\\), \\(\\dfrac{2}{3}=\\dfrac{70}{105}\\). Ordering smallest to largest: 45, 70, 84 gives \\(\\dfrac{3}{7}\\), \\(\\dfrac{2}{3}\\), \\(\\dfrac{4}{5}\\). Answer: option (3).",
"hints": ["Use a common denominator (LCM of 5, 7, 3 = 105).", "Compare the numerators after converting."],
"source": "Maris Stella 2023 P6 Prelim Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Fraction answers -> MCQ. Key = option (3)."
},
{
"n": 4,
"type_id": 1,
"question": "Which number is the largest?",
"answer0": "0.78",
"answer1": "0.87",
"answer2": "0.708",
"answer3": "0.807",
"correct_answer": 1,
"skill_id": 124,
"difficulty_id": 1,
"explanation": "Compare digit by digit. Tenths: 0.87 has 8, 0.807 has 8, 0.78 has 7, 0.708 has 7. Among the two with 8 tenths, hundredths: 0.87 has 7, 0.807 has 0. So 0.87 is the largest. Answer: 0.87.",
"hints": ["Line up the decimal points.", "Compare tenths first, then hundredths."],
"source": "Maris Stella 2023 P6 Prelim Q4",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key = option (2) = 0.87."
},
{
"n": 5,
"type_id": 1,
"question": "Express \\(3\\dfrac{2}{25}\\) as a decimal.",
"answer0": "3.2",
"answer1": "3.8",
"answer2": "3.08",
"answer3": "3.22",
"correct_answer": 2,
"skill_id": 158,
"difficulty_id": 2,
"explanation": "\\(\\dfrac{2}{25}=\\dfrac{8}{100}=0.08\\). So \\(3\\dfrac{2}{25}=3+0.08=3.08\\). Answer: 3.08.",
"hints": ["Make the denominator 100: multiply numerator and denominator by 4.", "\\(\\dfrac{8}{100}=0.08\\)."],
"source": "Maris Stella 2023 P6 Prelim Q5",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key = option (3) = 3.08."
},
{
"n": 6,
"type_id": 1,
"question": "Express 3080 cm in m.",
"answer0": "3.08 m",
"answer1": "3.8 m",
"answer2": "30.08 m",
"answer3": "30.8 m",
"correct_answer": 3,
"skill_id": 184,
"difficulty_id": 1,
"explanation": "100 cm = 1 m, so divide by 100: 3080 cm ÷ 100 = 30.8 m. Answer: 30.8 m.",
"hints": ["1 m = 100 cm.", "Divide the number of cm by 100."],
"source": "Maris Stella 2023 P6 Prelim Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key = option (4) = 30.8 m."
},
{
"n": 7,
"type_id": 1,
"question": "Round 3.465 to 2 decimal places.",
"answer0": "3.40",
"answer1": "3.46",
"answer2": "3.47",
"answer3": "3.50",
"correct_answer": 2,
"skill_id": 128,
"difficulty_id": 1,
"explanation": "To round to 2 decimal places, look at the 3rd decimal digit (5). Since it is 5, round up the 2nd decimal digit: 3.465 -> 3.47. Answer: 3.47.",
"hints": ["Look at the third decimal place.", "5 or more rounds the second decimal place up."],
"source": "Maris Stella 2023 P6 Prelim Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key = option (3) = 3.47."
},
{
"n": 8,
"type_id": 1,
"question": "In a basket, there were 4 apples, 8 pears and 12 papayas. What is the ratio of the number of apples to the total number of pears and papayas?",
"answer0": "1 : 5",
"answer1": "5 : 1",
"answer2": "1 : 2",
"answer3": "1 : 3",
"correct_answer": 0,
"skill_id": 180,
"difficulty_id": 1,
"explanation": "Pears + papayas = 8 + 12 = 20. Ratio of apples to (pears + papayas) = 4 : 20 = 1 : 5. Answer: 1 : 5.",
"hints": ["Add the pears and papayas first.", "Simplify the ratio 4 : 20."],
"source": "Maris Stella 2023 P6 Prelim Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Ratio answer -> MCQ. Key = option (1) = 1 : 5."
},
{
"n": 9,
"type_id": 1,
"question": "Which 2 lines are parallel to each other?",
"answer0": "AD and DG",
"answer1": "AG and BF",
"answer2": "AG and CE",
"answer3": "BF and CE",
"correct_answer": 3,
"skill_id": 100,
"difficulty_id": 2,
"explanation": "On the square grid, parallel lines have the same slope. Lines BF and CE both rise the same number of squares for every square across (same gradient), so they are parallel. Answer: BF and CE.",
"hints": ["Parallel lines have the same steepness (gradient) on the grid.", "Count the rise and run of each line."],
"source": "Maris Stella 2023 P6 Prelim Q9",
"image_needed": true,
"image_options": false,
"image_file": "q9.png",
"image_page": 5,
"image_bbox": [0.19, 0.12, 0.68, 0.42],
"image_loc": "grid with lines and points A,B,C,D,E,F,G near top of page",
"notes": "Key = option (4) = BF and CE."
},
{
"n": 10,
"type_id": 1,
"question": "Which of the following is a net of a cube?",
"answer0": "Net (1)",
"answer1": "Net (2)",
"answer2": "Net (3)",
"answer3": "Net (4)",
"correct_answer": 2,
"skill_id": 233,
"difficulty_id": 2,
"explanation": "A valid cube net must fold into a closed cube with no overlapping faces. Net (3) folds correctly into a cube; the others overlap or leave a face open. Answer: option (3).",
"hints": ["A cube net has exactly 6 squares.", "Mentally fold each option to see if it closes into a cube."],
"source": "Maris Stella 2023 P6 Prelim Q10",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 5,
"image_bbox": [0.18, 0.6, 0.85, 0.95],
"image_loc": "four candidate nets (1)-(4) in lower half of page",
"notes": "Image-option MCQ: each option is a net diagram. Key = option (3). Crop each option to q10_opt0..3.png."
},
{
"n": 11,
"type_id": 1,
"question": "The table shows the marks scored by 5 students in a test.
Students: A, B, C, D, E
Marks: 20, 30, 10, 20, 40
Which of the following bar graphs represents the information shown in the table?",
"answer0": "Bar graph (1)",
"answer1": "Bar graph (2)",
"answer2": "Bar graph (3)",
"answer3": "Bar graph (4)",
"correct_answer": 0,
"skill_id": 102,
"difficulty_id": 2,
"explanation": "The bars must show A=20, B=30, C=10, D=20, E=40. Graph (1) shows these exact heights with C the shortest and E the tallest, B taller than A and D which are equal. Answer: option (1).",
"hints": ["Match each bar height to the table value.", "C should be the shortest (10) and E the tallest (40)."],
"source": "Maris Stella 2023 P6 Prelim Q11",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 6,
"image_bbox": [0.18, 0.2, 0.85, 0.97],
"image_loc": "four bar graphs (1)-(4) stacked down the page",
"notes": "Image-option MCQ: each option is a bar graph. Key = option (1). Crop each option to q11_opt0..3.png."
},
{
"n": 12,
"type_id": 1,
"question": "In the figure, AB, CD and EF are straight lines. Find ∠AOF.",
"answer0": "42°",
"answer1": "45°",
"answer2": "48°",
"answer3": "87°",
"correct_answer": 0,
"skill_id": 194,
"difficulty_id": 2,
"explanation": "∠COE = 93° and ∠BOD = 45° (given). ∠DOF is vertically opposite ∠COE = 93°... Using angles on straight line AB: ∠AOF + ∠FOB = 180°, and ∠FOB = ∠COE = 93° (vert. opp. would be ∠EOA). Compute via vertically opposite: ∠AOF is vertically opposite ∠BOE. On line CD, ∠COE + ∠EOB = 180° so ∠EOB = 87°; ∠AOF = vert. opp. of... Final: ∠AOF = 180° − 93° − 45° = 42°. Answer: 42°.",
"hints": ["Use angles on a straight line (sum 180°) and vertically opposite angles.", "∠AOF = 180° − 93° − 45°."],
"source": "Maris Stella 2023 P6 Prelim Q12",
"image_needed": true,
"image_options": false,
"image_file": "q12.png",
"image_page": 7,
"image_bbox": [0.22, 0.1, 0.66, 0.3],
"image_loc": "X-shaped intersecting straight lines at O with 93 deg and 45 deg marked",
"notes": "Key = option (1) = 42°."
},
{
"n": 13,
"type_id": 1,
"question": "Tom and Jerry were standing at X, facing the same place at first. Tom turned 90° clockwise to face the Library and Jerry turned 225° anti-clockwise. Where will Jerry face in the end?",
"answer0": "Church",
"answer1": "Post Office",
"answer2": "Park",
"answer3": "School",
"correct_answer": 1,
"skill_id": 142,
"difficulty_id": 3,
"explanation": "The 8 directions are 45° apart. Tom turned 90° clockwise to face the Library, so initially both faced 90° anti-clockwise from the Library = Supermarket. Jerry turns 225° anti-clockwise from Supermarket: 225° = 5 steps of 45° anti-clockwise. Supermarket -> Church -> Playground -> Park -> Post Office -> ... lands on Post Office. Answer: Post Office.",
"hints": ["Each adjacent direction is 45° apart.", "Find the starting direction from Tom's turn, then rotate Jerry 225° (5 steps) anti-clockwise."],
"source": "Maris Stella 2023 P6 Prelim Q13",
"image_needed": true,
"image_options": false,
"image_file": "q13.png",
"image_page": 7,
"image_bbox": [0.28, 0.5, 0.72, 0.78],
"image_loc": "8-point compass diagram centred at X with place names and a North arrow at right",
"notes": "Key = option (2) = Post Office. Include the North arrow."
},
{
"n": 14,
"type_id": 1,
"question": "The table below shows the range of marks scored by a group of 220 students in a competition.
Marks: 70, 75, 80, 85, 90
Number of students: 24, 44, 108, 36, 8
20% of the students in this group qualified for the next round. What is the minimum score needed to qualify for the next round?",
"answer0": "75",
"answer1": "80",
"answer2": "85",
"answer3": "90",
"correct_answer": 2,
"skill_id": 175,
"difficulty_id": 3,
"explanation": "20% of 220 = 44 students qualify, i.e. the top 44 scorers. Counting from the highest: 90 has 8, 85 has 36; 8 + 36 = 44. So the top 44 scored 85 or 90. The minimum qualifying score is 85. Answer: 85.",
"hints": ["Find 20% of 220 = 44 students.", "Count from the highest score downwards until you reach 44 students."],
"source": "Maris Stella 2023 P6 Prelim Q14",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Table given in stem. Key = option (3) = 85."
},
{
"n": 15,
"type_id": 1,
"question": "At a party, 20% of the people were men, 55% of the remaining people were women and the rest were children. There were 100 men. How many children were there at the party?",
"answer0": "125",
"answer1": "180",
"answer2": "220",
"answer3": "500",
"correct_answer": 1,
"skill_id": 175,
"difficulty_id": 3,
"explanation": "Men = 20% = 100, so total people = 100 ÷ 0.2 = 500. Remaining = 500 − 100 = 400. Women = 55% of 400 = 220. Children = 400 − 220 = 180. Answer: 180.",
"hints": ["Use the 100 men (20%) to find the total number of people.", "Children = remaining people − women."],
"source": "Maris Stella 2023 P6 Prelim Q15",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key = option (2) = 180."
},
{
"n": 16,
"type_id": 2,
"question": "Find the value of (74 − 36) × 10 + 6 ÷ 2 = [?]",
"answer0": "383",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 155,
"difficulty_id": 1,
"explanation": "Brackets first: 74 − 36 = 38. Then × and ÷ before +: 38 × 10 = 380 and 6 ÷ 2 = 3. Finally 380 + 3 = 383. Answer: 383.",
"hints": ["Do the brackets first, then × and ÷, then +.", "38 × 10 = 380; 6 ÷ 2 = 3."],
"source": "Maris Stella 2023 P6 Prelim Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key Q16 = 383."
},
{
"n": 17,
"type_id": 2,
"question": "How many sixths are there in \\(5\\dfrac{1}{3}\\)? [?]",
"answer0": "32",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 206,
"difficulty_id": 2,
"explanation": "\\(5\\dfrac{1}{3}=\\dfrac{16}{3}=\\dfrac{32}{6}\\). So there are 32 sixths. Equivalently \\(5\\dfrac{1}{3}\\div\\dfrac{1}{6}=\\dfrac{16}{3}\\times 6=32\\). Answer: 32.",
"hints": ["Convert the mixed number to an improper fraction.", "Divide by \\(\\dfrac{1}{6}\\) (multiply by 6)."],
"source": "Maris Stella 2023 P6 Prelim Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer is a whole number (32). Key Q17 = 32."
},
{
"n": 18,
"type_id": 2,
"question": "Find the value of 12.2 − 5.47 = [?]",
"answer0": "6.73",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 129,
"difficulty_id": 1,
"explanation": "Align decimals: 12.20 − 5.47 = 6.73. Answer: 6.73.",
"hints": ["Write 12.2 as 12.20.", "Subtract column by column."],
"source": "Maris Stella 2023 P6 Prelim Q18",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key Q18 = 6.73."
},
{
"n": 19,
"type_id": 2,
"question": "How much water (in ml) is in the container? [?]",
"answer0": "26",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 184,
"difficulty_id": 2,
"explanation": "Read the water level against the scale on the measuring container. The water reaches the 26 ml mark. Answer: 26 ml.",
"hints": ["Read the level where the top of the water meets the scale.", "Note the value of each small marking."],
"source": "Maris Stella 2023 P6 Prelim Q19",
"image_needed": true,
"image_options": false,
"image_file": "q19.png",
"image_page": 12,
"image_bbox": [0.28, 0.14, 0.45, 0.42],
"image_loc": "measuring container with 50 ml mark, partially filled, upper-left of page",
"notes": "Answer in ml. Key Q19 = 26."
},
{
"n": 20,
"type_id": 0,
"question": "Given the line of symmetry line AB, shade 2 squares to complete the symmetric figure.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 145,
"difficulty_id": 2,
"explanation": "Reflect each already-shaded square across the diagonal line of symmetry AB. The 2 squares whose mirror images are not yet shaded must be shaded to make the figure symmetric (see answer-key diagram on Pg1).",
"hints": ["Each shaded square has a mirror image across line AB.", "Shade the squares needed so every shaded square has a shaded mirror partner."],
"source": "Maris Stella 2023 P6 Prelim Q20",
"image_needed": true,
"image_options": false,
"image_file": "q20.png",
"image_page": 12,
"image_bbox": [0.33, 0.52, 0.62, 0.78],
"image_loc": "4x4 grid with some shaded squares and a diagonal dashed line of symmetry AB",
"notes": "Interactive shade-the-figure task -> type_id 0 (skipped on insert). Answer is a shading shown in the answer key (Pg1 Q20 diagram)."
},
{
"n": 21,
"type_id": 1,
"question": "(a) Find the value of \\(1-\\dfrac{1}{3}-\\dfrac{1}{5}\\). (b) Find the value of \\(11\\div\\dfrac{3}{5}\\).",
"answer0": "(a) \\(\\dfrac{7}{15}\\) (b) \\(18\\dfrac{1}{3}\\)",
"answer1": "(a) \\(\\dfrac{8}{15}\\) (b) \\(18\\dfrac{1}{3}\\)",
"answer2": "(a) \\(\\dfrac{7}{15}\\) (b) \\(6\\dfrac{3}{5}\\)",
"answer3": "(a) \\(\\dfrac{2}{3}\\) (b) \\(18\\dfrac{1}{3}\\)",
"correct_answer": 0,
"skill_id": 159,
"difficulty_id": 2,
"explanation": "(a) Common denominator 15: \\(1=\\dfrac{15}{15}\\), so \\(\\dfrac{15}{15}-\\dfrac{5}{15}-\\dfrac{3}{15}=\\dfrac{7}{15}\\). (b) \\(11\\div\\dfrac{3}{5}=11\\times\\dfrac{5}{3}=\\dfrac{55}{3}=18\\dfrac{1}{3}\\). Answers: \\(\\dfrac{7}{15}\\) and \\(18\\dfrac{1}{3}\\).",
"hints": ["(a) Use a common denominator of 15.", "(b) Dividing by a fraction = multiplying by its reciprocal."],
"source": "Maris Stella 2023 P6 Prelim Q21",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Fraction/mixed-number answers -> MCQ. Key Q21a = 7/15, Q21b = 18 1/3. Both parts combined into one correct option (0)."
},
{
"n": 22,
"type_id": 2,
"question": "Denise answered 20 questions in a survey. She took 3 min for each of the first 10 questions and twice as long for each of the remaining questions. She started her survey at 1.20 p.m. At what time did she complete her survey? [?] p.m.",
"answer0": "2.50",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 93,
"difficulty_id": 2,
"explanation": "First 10 questions: 10 × 3 = 30 min. Remaining 10 questions: 6 min each, 10 × 6 = 60 min. Total = 30 + 60 = 90 min = 1 h 30 min. Start 1.20 p.m. + 1 h 30 min = 2.50 p.m. Answer: 2.50 p.m.",
"hints": ["Twice as long as 3 min is 6 min per remaining question.", "Add the total minutes to the start time."],
"source": "Maris Stella 2023 P6 Prelim Q22",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer is a clock time (2.50). Unit p.m. shown in stem. Key Q22 = 2.50 p.m."
},
{
"n": 23,
"type_id": 2,
"question": "From the figure, what is the minimum number of unit cubes that needs to be added to form a cuboid? [?]",
"answer0": "23",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 188,
"difficulty_id": 3,
"explanation": "The smallest cuboid that contains the given solid is determined by its overall length, breadth and height. The number of cubes needed to fill that bounding cuboid minus the cubes already present gives 23. Answer: 23.",
"hints": ["Find the dimensions of the smallest cuboid that encloses the figure.", "Subtract the cubes already shown from the full cuboid's volume."],
"source": "Maris Stella 2023 P6 Prelim Q23",
"image_needed": true,
"image_options": false,
"image_file": "q23.png",
"image_page": 14,
"image_bbox": [0.15, 0.14, 0.55, 0.36],
"image_loc": "isometric arrangement of unit cubes (L/staircase shape) upper part of page",
"notes": "Key Q23 = 23. Crop must show whole cube arrangement to verify count."
},
{
"n": 24,
"type_id": 2,
"question": "The ratio of the number of stickers Kingston had to the number of stickers Tim had was 8 : 5. After Kingston gave away 44 stickers, Tim had twice as many stickers as Kingston. How many stickers did they have at first? [?]",
"answer0": "104",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 214,
"difficulty_id": 3,
"explanation": "Let Kingston = 8u, Tim = 5u. After giving away 44, Tim = 2 × (new Kingston): 5u = 2(8u − 44) = 16u − 88, so 88 = 11u, u = 8. Total at first = 8u + 5u = 13u = 13 × 8 = 104. Answer: 104.",
"hints": ["Use units: Kingston = 8u, Tim = 5u.", "After Kingston gives 44 away, Tim = 2 × Kingston's new amount."],
"source": "Maris Stella 2023 P6 Prelim Q24",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key Q24 = 104 (total at first)."
},
{
"n": 25,
"type_id": 2,
"question": "Pauline drove from her home to her office. The distance between her home and her office was 24 km. The average speed of her car was 60 km/h. Pauline left home at 0815, what time did she reach her office? [?]",
"answer0": "0839",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 217,
"difficulty_id": 2,
"explanation": "Time = distance ÷ speed = 24 ÷ 60 = 0.4 h = 24 min. Start 0815 + 24 min = 0839. Answer: 0839.",
"hints": ["Time = distance ÷ speed.", "0.4 h = 24 minutes; add to 0815."],
"source": "Maris Stella 2023 P6 Prelim Q25",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer is a 24-hour clock time (0839). Key Q25 = 0839."
},
{
"n": 26,
"type_id": 0,
"question": "The pie chart shows the favourite snacks of students in School A and B. 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: An equal number of students in School A and School B chose candy as their favourite snack. Statement 2: \\(\\dfrac{3}{4}\\) of the students in School B chose chocolates and candy as their favourite snacks.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 235,
"difficulty_id": 3,
"explanation": "Statement 1: Both schools show candy = 20%, but the total number of students in each school is unknown, so an equal number cannot be confirmed — Not possible to tell. Statement 2: School B chocolates = 1/2 and candy = 20% = 1/5; 1/2 + 1/5 = 7/10, not 3/4 — False. Answers: Not possible to tell; False.",
"hints": ["Percentages equal does not mean equal counts unless totals are equal.", "Add School B's chocolate (1/2) and candy (1/5) fractions."],
"source": "Maris Stella 2023 P6 Prelim Q26",
"image_needed": true,
"image_options": false,
"image_file": "q26.png",
"image_page": 15,
"image_bbox": [0.12, 0.42, 0.85, 0.65],
"image_loc": "two pie charts (School A and School B) with Candy/Potato chips/Jelly/Chocolates segments",
"notes": "True/False/NPTT tick-table -> type_id 0 (skipped on insert). Key: Statement 1 = Not possible to tell; Statement 2 = False."
},
{
"n": 27,
"type_id": 0,
"question": "A parallelogram, ABCD is drawn on a square grid. (a) Draw a triangle that is \\(\\dfrac{1}{2}\\) the area of the parallelogram ABCD. Label it EFG. (b) Draw a parallelogram that has twice the perimeter as the parallelogram ABCD. Label it WXYZ. Both triangle EFG and parallelogram WXYZ should not overlap parallelogram ABCD and each other.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 201,
"difficulty_id": 3,
"explanation": "(a) Triangle EFG must have area = 1/2 of parallelogram ABCD's area (e.g. a triangle with the same base and height as ABCD, since triangle area = 1/2 base × height). (b) Parallelogram WXYZ must have each side double ABCD's so its perimeter is twice. Drawn on the grid not overlapping ABCD (see answer-key diagram on Pg2 Q27).",
"hints": ["A triangle with the same base and height as a parallelogram has half its area.", "Doubling each side length doubles the perimeter."],
"source": "Maris Stella 2023 P6 Prelim Q27",
"image_needed": true,
"image_options": false,
"image_file": "q27.png",
"image_page": 16,
"image_bbox": [0.18, 0.27, 0.83, 0.66],
"image_loc": "square grid with parallelogram ABCD drawn",
"notes": "Drawing/construction task -> type_id 0 (skipped on insert). Answer is a construction shown in the answer key (Pg2 Q27 diagram)."
},
{
"n": 28,
"type_id": 1,
"question": "Andy had $5x. After buying apples at 60¢ each, he had $2x left. How many apples did Andy buy?",
"answer0": "\\(\\dfrac{3x}{0.6}\\)",
"answer1": "\\(\\dfrac{2x}{0.6}\\)",
"answer2": "\\(\\dfrac{5x}{0.6}\\)",
"answer3": "\\(5x\\)",
"correct_answer": 0,
"skill_id": 241,
"difficulty_id": 3,
"explanation": "Money spent on apples = $5x − $2x = $3x. Each apple costs 60¢ = $0.60. Number of apples = \\(\\dfrac{3x}{0.6}\\). Answer: \\(\\dfrac{3x}{0.6}\\) (= 5x).",
"hints": ["Amount spent = starting amount − amount left.", "Number of apples = amount spent ÷ price per apple."],
"source": "Maris Stella 2023 P6 Prelim Q28",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Algebraic answer -> MCQ. Key Q28 = 3x/0.6 (equivalently 5x)."
},
{
"n": 29,
"type_id": 2,
"question": "Benedict has 2 cubical tanks, A and B. The large cubical tank A has twice the length, twice the breadth and twice the height of the small cubical tank B. The small cubical tank B is filled completely with 8 identical cubes, how many of such cubes is needed to fill the large cubical tank A completely? [?]",
"answer0": "64",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 229,
"difficulty_id": 3,
"explanation": "Doubling each of the 3 dimensions multiplies the volume by 2 × 2 × 2 = 8. So tank A holds 8 times as many cubes as tank B: 8 × 8 = 64 cubes. Answer: 64.",
"hints": ["Volume scales by the cube of the linear scale factor.", "Tank A volume = 8 × tank B volume."],
"source": "Maris Stella 2023 P6 Prelim Q29",
"image_needed": true,
"image_options": false,
"image_file": "q29.png",
"image_page": 17,
"image_bbox": [0.15, 0.16, 0.5, 0.32],
"image_loc": "two cubes labelled A (large) and B (small) upper part of page",
"notes": "Key Q29 = 64."
},
{
"n": 30,
"type_id": 2,
"question": "In the figure, DEF is a straight line. ∠DEH = 150° and ∠GEF = 110°. Find ∠GEH. [?]",
"answer0": "80",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 194,
"difficulty_id": 2,
"explanation": "∠DEH + ∠HEF = 180° (angles on straight line DEF), so ∠HEF = 30°. ∠GEH = ∠GEF − ∠HEF = 110° − 30° = 80°. Answer: 80°.",
"hints": ["∠DEH and ∠HEF are angles on a straight line (sum 180°).", "∠GEH = ∠GEF − ∠HEF."],
"source": "Maris Stella 2023 P6 Prelim Q30",
"image_needed": true,
"image_options": false,
"image_file": "q30.png",
"image_page": 17,
"image_bbox": [0.18, 0.55, 0.66, 0.74],
"image_loc": "straight line DEF with rays EG and EH, 150 deg and 110 deg marked",
"notes": "Answer in degrees (80). Key Q30 = 80."
},
{
"n": 31,
"type_id": 2,
"question": "The pie chart shows how Michael spent his money. Toy = $38, Lunch = $10, Movie = $12, and the Book segment is a right angle. (a) How much money did Michael spend on the book? $[?] (b) What percentage of Michael's money was spent on lunch? [?]%",
"answer0": "20",
"answer1": "12.5",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 236,
"difficulty_id": 2,
"explanation": "Lunch percentage: total money — the book is a right angle = 90° = 1/4 = 25% of the circle. (b) Lunch $10 is 12.5% of total, so total = 10 ÷ 0.125 = $80. (a) Book = 25% of $80 = $20. Answers: (a) $20, (b) 12.5%.",
"hints": ["The right-angle book segment is 1/4 (25%) of the whole circle.", "Total = $80 (from Toy 38 + Lunch 10 + Movie 12 + Book 20)."],
"source": "Maris Stella 2023 P6 Prelim P2 Q1",
"image_needed": true,
"image_options": false,
"image_file": "q31.png",
"image_page": 21,
"image_bbox": [0.18, 0.18, 0.62, 0.45],
"image_loc": "pie chart with Toy $38, Book, Lunch $10, Movie $12, Chocolates segments",
"notes": "Paper 2 Q1. Both answers numeric -> FIB. Key P2 Q1a = $20, Q1b = 12.5%."
},
{
"n": 32,
"type_id": 2,
"question": "The bar graph shows the number of cups of ice cream sold in a shop. Monday = 250, Tuesday = 180, Wednesday = 300, Thursday = 230. What is the average number of cups of ice cream sold each day? [?]",
"answer0": "240",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 203,
"difficulty_id": 2,
"explanation": "Total = 250 + 180 + 300 + 230 = 960. Average = 960 ÷ 4 = 240 cups. Answer: 240.",
"hints": ["Add the cups for all 4 days.", "Average = total ÷ number of days."],
"source": "Maris Stella 2023 P6 Prelim P2 Q2",
"image_needed": true,
"image_options": false,
"image_file": "q32.png",
"image_page": 22,
"image_bbox": [0.15, 0.12, 0.85, 0.37],
"image_loc": "bar graph of cups sold Mon-Thu in upper part of page",
"notes": "Paper 2 Q2. Key = 240. Bar values read from graph (Mon 250, Tue 180, Wed 300, Thu 230)."
},
{
"n": 33,
"type_id": 2,
"question": "Jimmy gave his mother $1200 of his salary. He gave \\(\\dfrac{5}{8}\\) of the remainder of his salary to his brother and had \\(\\dfrac{1}{4}\\) of his salary left. What was Jimmy's salary? $[?]",
"answer0": "3600",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "After giving the brother \\(\\dfrac{5}{8}\\) of the remainder, \\(\\dfrac{3}{8}\\) of the remainder is left, which equals \\(\\dfrac{1}{4}\\) of the salary. So remainder = $1200 corresponds to: \\(\\dfrac{3}{8}\\) of remainder = \\(\\dfrac{1}{4}\\) salary. The $1200 given to mother is \\(\\dfrac{1}{3}\\) of the salary, so salary = 1200 × 3 = $3600. Answer: $3600.",
"hints": ["3/8 of the remainder = 1/4 of the salary left.", "The $1200 to mother turns out to be 1/3 of the salary."],
"source": "Maris Stella 2023 P6 Prelim P2 Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q3. Key = $3600."
},
{
"n": 34,
"type_id": 1,
"question": "The graph shows the number of toys sold by a shop from March to June. March = 20, April = 40, May = 50, June = 80. In which 1-month interval was the percentage increase of toys sold the most?",
"answer0": "March to April",
"answer1": "April to May",
"answer2": "May to June",
"answer3": "March to June",
"correct_answer": 0,
"skill_id": 208,
"difficulty_id": 3,
"explanation": "Percentage increase each month: Mar->Apr = (40−20)/20 = 100%; Apr->May = (50−40)/40 = 25%; May->Jun = (80−50)/50 = 60%. The greatest is March to April (100%). Answer: March to April.",
"hints": ["Percentage increase = (increase ÷ original) × 100%.", "Compare the percentage, not the raw increase."],
"source": "Maris Stella 2023 P6 Prelim P2 Q4",
"image_needed": true,
"image_options": false,
"image_file": "q34.png",
"image_page": 23,
"image_bbox": [0.18, 0.13, 0.82, 0.42],
"image_loc": "line graph of number of toys Mar-Jun in upper part of page",
"notes": "Paper 2 Q4. Answer is an interval (word) -> MCQ. Key = March to April."
},
{
"n": 35,
"type_id": 2,
"question": "A 1 m wide path cuts across a rectangular field along its length and breadth, forming a path. The field is 18 m by 8 m and the path is 1 m wide. What is the area of the path? [?] m²",
"answer0": "25",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Path along length = 18 × 1 = 18 m². Path along breadth = 8 × 1 = 8 m². They overlap in a 1 × 1 = 1 m² square (counted twice). Area of path = 18 + 8 − 1 = 25 m². Answer: 25 m².",
"hints": ["Add the two strips: 18×1 and 8×1.", "Subtract the 1×1 m² overlap counted twice."],
"source": "Maris Stella 2023 P6 Prelim P2 Q5",
"image_needed": true,
"image_options": false,
"image_file": "q35.png",
"image_page": 24,
"image_bbox": [0.2, 0.16, 0.78, 0.32],
"image_loc": "rectangle 18 m by 8 m with a 1 m wide cross-path shaded",
"notes": "Paper 2 Q5. Answer in m² (25). Key = 25."
},
{
"n": 36,
"type_id": 2,
"question": "Mr Lee had a piece of wire 26y cm long. He used the wire to form a rectangle, with length and breadth measuring 2y cm and 20 cm. (a) Express the length of the remaining wire in terms of y. [?] (b) Mr Lee used the remaining wire to make a square. If y = 4, what was the length of one side of the square? [?] cm",
"answer0": "(22y − 40)",
"answer1": "12",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 241,
"difficulty_id": 3,
"explanation": "(a) Perimeter of rectangle = 2(2y + 20) = 4y + 40. Remaining wire = 26y − (4y + 40) = 22y − 40 cm. (b) When y = 4: remaining = 22(4) − 40 = 88 − 40 = 48 cm. A square has 4 equal sides, so one side = 48 ÷ 4 = 12 cm. Answers: (a) (22y − 40) cm, (b) 12 cm.",
"hints": ["Rectangle perimeter = 2 × (length + breadth).", "Square side = remaining wire ÷ 4."],
"source": "Maris Stella 2023 P6 Prelim P2 Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q6. (a) is an algebraic expression answer; (b) numeric (12). Key Q6a = 22y − 40, Q6b = 12 cm. answer0 holds the algebraic (a); accept '22y-40'."
},
{
"n": 37,
"type_id": 2,
"question": "The diagram shows 4 identical right-angled isosceles triangles with a quadrant within it. The quadrant has a radius of 7.5 cm. (Take π = 3.14) Find the area of the shaded part. [?] cm²",
"answer0": "48.375",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 221,
"difficulty_id": 3,
"explanation": "Quadrant area = \\(\\dfrac{1}{4}\\times 3.14\\times 7.5\\times 7.5 = 44.15625\\)... using the key's method: one triangle has base/height 7.5×2 = 15, area of the relevant region 15×... Key: 3.14 × 7.5 × 7.5 = 176.625 (this is the full circle of r=7.5). The 4 triangles area: base 15, total 225. Shaded = 225 − 176.625 = 48.375 cm². Answer: 48.375 cm².",
"hints": ["Find the total area of the triangles.", "Subtract the circular (quadrant) region from the triangles' area."],
"source": "Maris Stella 2023 P6 Prelim P2 Q7",
"image_needed": true,
"image_options": false,
"image_file": "q37.png",
"image_page": 25,
"image_bbox": [0.18, 0.5, 0.6, 0.62],
"image_loc": "row of 4 right-angled isosceles triangles with a quadrant/curve inside",
"notes": "Paper 2 Q7. Answer in cm² (48.375). Key = 48.375."
},
{
"n": 38,
"type_id": 2,
"question": "The figure shows a square ABCD. EH = EF = EG. Find ∠FGH. [?]",
"answer0": "150",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "Using the equal lengths EH = EF = EG and the angle properties of the square, the working gives ∠FGH = 180° − 30° = 150°. Answer: 150°.",
"hints": ["Use the isosceles triangles formed by the equal sides EH = EF = EG.", "Combine with the right angles of the square ABCD."],
"source": "Maris Stella 2023 P6 Prelim P2 Q8",
"image_needed": true,
"image_options": false,
"image_file": "q38.png",
"image_page": 26,
"image_bbox": [0.25, 0.15, 0.62, 0.4],
"image_loc": "square ABCD with point E on top side and triangles to H, F, G",
"notes": "Paper 2 Q8. Answer in degrees (150). Key working: 180 − 30 = 150."
},
{
"n": 39,
"type_id": 2,
"question": "At 8 a.m., Joey travelled from Town X to Town Y at a constant speed of 120 km/h. At the same time, Madeline travelled from Town Y to Town X at a constant speed of 90 km/h. At 9.20 a.m., they were 50 km apart after driving past each other. What is the distance between Town X and Town Y? [?] km",
"answer0": "230",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 219,
"difficulty_id": 3,
"explanation": "Time travelled = 8 a.m. to 9.20 a.m. = 1 h 20 min = \\(1\\dfrac{1}{3}\\) h. Joey's distance = 120 × 4/3 = 160 km. Madeline's distance = 90 × 4/3 = 120 km. They have passed each other and are 50 km apart, so distance XY = 160 + 120 − 50 = 230 km. Answer: 230 km.",
"hints": ["1 h 20 min = 4/3 h.", "After passing, total distance = sum of distances − the 50 km gap."],
"source": "Maris Stella 2023 P6 Prelim P2 Q9",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q9. Answer in km (230). Key = 230."
},
{
"n": 40,
"type_id": 2,
"question": "X is a cubical tank of sides 20 cm and Y is a rectangular tank. The base of Y is 60 cm by 20 cm. X was fully filled with water and Y was empty. Samuel poured some water from X into Y without spilling. After that, the heights of the water level of X and Y were the same. What was the final height of the water level in both tanks? [?] cm",
"answer0": "5",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 229,
"difficulty_id": 3,
"explanation": "Total water = volume of X = 20³ = 8000 cm³. The water sits at the same height h in both tanks. Base area X = 20 × 20 = 400; base area Y = 60 × 20 = 1200. Combined base area = 400 + 1200 = 1600 cm². Height = 8000 ÷ 1600 = 5 cm. Answer: 5 cm.",
"hints": ["All the water comes from tank X (20³ = 8000 cm³).", "Same height means total volume ÷ combined base area (400 + 1200)."],
"source": "Maris Stella 2023 P6 Prelim P2 Q10",
"image_needed": true,
"image_options": false,
"image_file": "q40.png",
"image_page": 28,
"image_bbox": [0.15, 0.14, 0.78, 0.36],
"image_loc": "cube X (sides 20 cm) and cuboid Y (base 60 cm by 20 cm) upper part of page",
"notes": "Paper 2 Q10. Answer in cm (5). Key = 5."
},
{
"n": 41,
"type_id": 2,
"question": "The table shows the scores of 4 students in a Math test. Some of the scores are covered by an ink patch.
Aloysius = 6_, Benedict = 8_, Charles = 7_, Dominic = 82.
The average score of Charles and Dominic is 80. The average score of Aloysius, Benedict and Charles is 74. What is the largest possible score that Benedict has achieved? [?]",
"answer0": "84",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 205,
"difficulty_id": 3,
"explanation": "Charles + Dominic = 80 × 2 = 160, and Dominic = 82, so Charles = 78. Aloysius + Benedict + Charles = 74 × 3 = 222, so Aloysius + Benedict = 222 − 78 = 144. Aloysius is 6_ (smallest possible 60) to make Benedict largest: Benedict = 144 − 60 = 84. Answer: 84.",
"hints": ["Use the averages to find Charles (78) first.", "To make Benedict largest, make Aloysius as small as possible (60)."],
"source": "Maris Stella 2023 P6 Prelim P2 Q11",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q11. Table in stem; ink-patch digits shown as 6_, 8_, 7_. Key = 84."
},
{
"n": 42,
"type_id": 2,
"question": "Peter had some stickers. He gave half of them and an additional 60 stickers to Samuel. Next, he gave half of the remainder of the stickers and an additional 30 stickers to Troy. He then gave 40 stickers to each of his 3 siblings and had 100 stickers left. How many stickers did Peter have at first? [?]",
"answer0": "1120",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Work backwards. After siblings: 100 + 3×40 = 100 + 120 = 220 before the siblings. Before Troy: (220 + 30) × 2 = 250 × 2 = 500. Before Samuel: (500 + 60) × 2 = 560 × 2 = 1120. Answer: 1120. (Key working: 120 + 30 + 100 = 250; 60 + 250 + 250 = 560; 560 × 2 = 1120.)",
"hints": ["Work backwards from the 100 left.", "Reverse each step: undo the '+40 to 3 siblings', then Troy, then Samuel."],
"source": "Maris Stella 2023 P6 Prelim P2 Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q12. Key = 1120."
},
{
"n": 43,
"type_id": 2,
"question": "There were 400 adults attending a concert in a stadium. During the break, \\(\\dfrac{1}{3}\\) of the men and \\(\\dfrac{3}{5}\\) of the women left the stadium. 224 adults remained in the stadium. How many women were there in the stadium at first? [?]",
"answer0": "160",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Let m = men, w = women, m + w = 400. Remaining = \\(\\dfrac{2}{3}m + \\dfrac{2}{5}w = 224\\). Multiply by 3/2: m + \\(\\dfrac{3}{5}w = 336\\). Subtract from m + w = 400: \\(\\dfrac{2}{5}w = 64\\), so \\(\\dfrac{1}{5}w = 32\\), w = 160. Answer: 160 women.",
"hints": ["Set up men + women = 400 and the 'remained' equation.", "Eliminate men to solve for women."],
"source": "Maris Stella 2023 P6 Prelim P2 Q13",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q13. Key = 160 (women at first)."
},
{
"n": 44,
"type_id": 2,
"question": "In the figure, a rectangular piece of paper is folded twice. ∠GDA = 36° and ∠ADE = 10°. (a) Find ∠DAF. [?] (b) Find ∠DFE. [?]",
"answer0": "54",
"answer1": "77",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "(a) ∠DAF: since the corner of the rectangle is 90° and ∠GDA = 36°, ∠DAF = 90° − 36° = 54°. (b) ∠EDF = (36° − 10°) ÷ 2 = 13° (the fold bisects). In triangle DEF the right angle gives ∠DFE = 90° − 13° = 77°. Answers: (a) 54°, (b) 77°.",
"hints": ["(a) Use the 90° corner of the rectangle minus ∠GDA.", "(b) The fold bisects the angle; then use the right angle."],
"source": "Maris Stella 2023 P6 Prelim P2 Q14",
"image_needed": true,
"image_options": false,
"image_file": "q44.png",
"image_page": 32,
"image_bbox": [0.18, 0.16, 0.7, 0.36],
"image_loc": "rectangle GABC...D with folds to E and F near top of page",
"notes": "Paper 2 Q14. Both answers numeric degrees. Key Q14a = 54, Q14b = 77."
},
{
"n": 45,
"type_id": 2,
"question": "In the morning, Mrs Chen baked muffins of 3 different flavours — chocolate, strawberry and vanilla. The ratio of the number of chocolate muffins to the number of strawberry muffins was 3 : 5. There were 28 more strawberry muffins than chocolate muffins. There were 10 more vanilla muffins than strawberry muffins. How many vanilla muffins did she bake in the morning? [?]",
"answer0": "80",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 183,
"difficulty_id": 2,
"explanation": "Chocolate : strawberry = 3 : 5, difference = 2 units = 28, so 1 unit = 14. Strawberry = 5 × 14 = 70. Vanilla = strawberry + 10 = 70 + 10 = 80. Answer: 80 vanilla muffins.",
"hints": ["The 28 difference equals 2 units of the ratio.", "Find strawberry, then add 10 for vanilla."],
"source": "Maris Stella 2023 P6 Prelim P2 Q15a",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q15(a). Key = 80."
},
{
"n": 46,
"type_id": 2,
"question": "Mrs Chen baked chocolate, strawberry and vanilla muffins. In the morning there were 42 chocolate, 70 strawberry and 80 vanilla muffins. In the afternoon, she baked some more chocolate and vanilla muffins. The total number of chocolate and vanilla muffins became thrice the number of strawberry muffins. The percentage increase of the chocolate muffins was between 8% to 10%. How many vanilla muffins did she bake in the afternoon? [?]",
"answer0": "84",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 209,
"difficulty_id": 3,
"explanation": "Strawberry stays 70, so chocolate + vanilla total = 3 × 70 = 210. Chocolate increase 8–10% of 42 is 3.36–4.2, so chocolate increased by 4 (42 → 46). Vanilla total = 210 − 46 = 164. Vanilla baked in afternoon = 164 − 80 = 84. Answer: 84. (Key: 70×3 = 210; 8% = 3.20, 10% = 4.20, so +4 → 46; 210 − 46 − 80 = 84.)",
"hints": ["Total chocolate + vanilla = 3 × strawberry (210).", "Chocolate rose by a whole number that is 8–10% of 42 (i.e. 4)."],
"source": "Maris Stella 2023 P6 Prelim P2 Q15b",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q15(b). Morning counts carried from Q15a (choc 42, straw 70, van 80). Key = 84."
},
{
"n": 47,
"type_id": 2,
"question": "The figure shows a circle and 6 identical quarter circles. The radius of each quarter circle is 8 cm. Line XY passes through the centre of the circle. (Take π = 3.14) Find the area of the shaded part. [?] cm²",
"answer0": "150.72",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 222,
"difficulty_id": 3,
"explanation": "Area of one quarter circle = \\(\\dfrac{1}{4}\\times 3.14\\times 8\\times 8 = 50.24\\) cm². The big circle has diameter = 8 × 3 = 24, radius 12, area = 12 × 12 × 3.14 = 452.16 cm². 6 quarter circles total = 50.24 × 6 = 301.44 cm². Shaded area = 452.16 − 301.44 = 150.72 cm². Answer: 150.72 cm². (Answer key typo writes '15072'; correct value 150.72.)",
"hints": ["Quarter circle area = 1/4 × π × 8 × 8.", "Big circle radius = 12; shaded = big circle − 6 quarter circles."],
"source": "Maris Stella 2023 P6 Prelim P2 Q16a",
"image_needed": true,
"image_options": false,
"image_file": "q47.png",
"image_page": 34,
"image_bbox": [0.28, 0.13, 0.62, 0.33],
"image_loc": "large circle with 6 quarter circles and line XY through centre, shaded region",
"notes": "Paper 2 Q16(a). Answer in cm² (150.72). Answer-key value misprinted as 15072; corrected to 150.72 per working 452.16 − 301.44."
},
{
"n": 48,
"type_id": 2,
"question": "The figure shows a circle and 6 identical quarter circles. The radius of each quarter circle is 8 cm. Line XY passes through the centre of the circle. (Take π = 3.14) Find the perimeter of the shaded part. [?] cm",
"answer0": "166.72",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 222,
"difficulty_id": 3,
"explanation": "Circumference of big circle (radius 12) = 3.14 × 24 = 75.36 cm. Each quarter-circle arc = \\(\\dfrac{1}{4}\\times 3.14\\times 16 = 12.56\\) cm; 6 arcs = 75.36 cm. Perimeter = 75.36 × 2 = 150.72, plus the line XY (the two radii) 8 + 8 = 16: 150.72 + 8 + 8 = 166.72 cm. Answer: 166.72 cm.",
"hints": ["Big circle circumference = π × diameter (24).", "Add the 6 quarter-circle arcs and the line XY (8 + 8)."],
"source": "Maris Stella 2023 P6 Prelim P2 Q16b",
"image_needed": true,
"image_options": false,
"image_file": "q48.png",
"image_page": 34,
"image_bbox": [0.28, 0.13, 0.62, 0.33],
"image_loc": "same circle-and-6-quarter-circles figure as Q16(a)",
"notes": "Paper 2 Q16(b). Answer in cm (166.72). Same figure as previous question."
},
{
"n": 49,
"type_id": 1,
"question": "In June, Mr Tan saved 20% of his salary. In July, his monthly salary increased by $600 and he saved 15% of his new monthly salary. Given that Mr Tan saved the same amount of money in both months, find the percentage increase in Mr Tan's salary.",
"answer0": "\\(33\\dfrac{1}{3}\\)%",
"answer1": "30%",
"answer2": "25%",
"answer3": "20%",
"correct_answer": 0,
"skill_id": 208,
"difficulty_id": 3,
"explanation": "15% of $600 = $90, which is the extra 'saving slack' — set up: June saving 20% of S = July saving 15% of (S + 600). So 0.20S = 0.15(S + 600) → 0.20S = 0.15S + 90 → 0.05S = 90 → S = $1800. Increase = 600/1800 = \\(33\\dfrac{1}{3}\\)%. Answer: \\(33\\dfrac{1}{3}\\)%.",
"hints": ["Set June's saving (20% of salary) equal to July's (15% of salary + 600).", "Percentage increase = 600 ÷ original salary × 100%."],
"source": "Maris Stella 2023 P6 Prelim P2 Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q17. Answer is a mixed-number percentage -> MCQ. Key = 33 1/3%."
}
]
}