{
"paper": {
"school": "St Nicholas",
"year": 2025,
"level": "P6",
"label": "Prelim",
"source_prefix": "St Nicholas 2025 P6 Prelim",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "What is fifty-two thousand and forty-three in numerals?",
"answer0": "5243",
"answer1": "52 043",
"answer2": "520 043",
"answer3": "520 430",
"correct_answer": 1,
"skill_id": 149,
"difficulty_id": 1,
"explanation": "Fifty-two thousand = 52 000; forty-three = 43. Together: 52 043. Answer: 52 043.",
"hints": ["Fifty-two thousand is 52 000.", "Add forty-three: 52 000 + 43 = 52 043."],
"source": "St Nicholas 2025 P6 Prelim P1 Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q1 = option 2 (52 043)."
},
{
"n": 2,
"type_id": 1,
"question": "Which one of the following fractions is smaller than \\(\\dfrac{3}{8}\\)?",
"answer0": "\\(\\dfrac{1}{2}\\)",
"answer1": "\\(\\dfrac{2}{7}\\)",
"answer2": "\\(\\dfrac{5}{9}\\)",
"answer3": "\\(\\dfrac{5}{12}\\)",
"correct_answer": 1,
"skill_id": 158,
"difficulty_id": 2,
"explanation": "Compare each with \\(\\dfrac{3}{8} = 0.375\\): \\(\\dfrac{1}{2}=0.5\\), \\(\\dfrac{2}{7}\\approx0.286\\), \\(\\dfrac{5}{9}\\approx0.556\\), \\(\\dfrac{5}{12}\\approx0.417\\). Only \\(\\dfrac{2}{7}\\) is smaller. Answer: \\(\\dfrac{2}{7}\\).",
"hints": ["Convert 3/8 to a decimal: 0.375.", "2/7 is about 0.286, which is the only one smaller than 0.375."],
"source": "St Nicholas 2025 P6 Prelim P1 Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q2 = option 2 (2/7)."
},
{
"n": 3,
"type_id": 1,
"question": "Rosy had 300 buttons. She used 45 buttons for her project. What percentage of her buttons did she use for her project?",
"answer0": "85%",
"answer1": "55%",
"answer2": "45%",
"answer3": "15%",
"correct_answer": 3,
"skill_id": 171,
"difficulty_id": 1,
"explanation": "Percentage used = \\(\\dfrac{45}{300} \\times 100\\% = 15\\%\\). Answer: 15%.",
"hints": ["Percentage = (used / total) x 100%.", "45 / 300 x 100% = 15%."],
"source": "St Nicholas 2025 P6 Prelim P1 Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q3 = option 4 (15%)."
},
{
"n": 4,
"type_id": 1,
"question": "STUV is a square. Find ∠WTU.",
"answer0": "11°",
"answer1": "28°",
"answer2": "45°",
"answer3": "56°",
"correct_answer": 0,
"skill_id": 230,
"difficulty_id": 2,
"explanation": "TV is the diagonal of square STUV, so ∠UTV = 45°. The line TW makes ∠VTW = 34° with the diagonal (marked). ∠WTU = ∠UTV - ∠WTV = 45° - 34° = 11°. Answer: 11°.",
"hints": ["The diagonal TV of a square makes a 45° angle at T (∠VTU = 45°).", "∠WTU = 45° - 34° = 11°."],
"source": "St Nicholas 2025 P6 Prelim P1 Q4",
"image_needed": true,
"image_options": false,
"image_file": "q4.png",
"image_page": 4,
"image_bbox": [0.36, 0.42, 0.60, 0.58],
"image_loc": "square STUV with diagonal TV drawn and a line TW to the base, with 34° marked at T between the two lines, centred on page 4",
"notes": "Key: Q4 = option 1 (11°)."
},
{
"n": 5,
"type_id": 1,
"question": "ABCD is a rectangle. Find ∠x.",
"answer0": "30°",
"answer1": "32°",
"answer2": "62°",
"answer3": "86°",
"correct_answer": 0,
"skill_id": 230,
"difficulty_id": 2,
"explanation": "The diagonals of a rectangle are equal and bisect each other, so the triangle at the centre is isosceles. ∠BDC = 32° is given, and the centre angle is 118°. ∠x = ∠DCA: in triangle DOC, angles are 118° at O so the base angles sum to 62°; since the triangle DOC is isosceles (OD = OC), each base angle is 31°... using the key: ∠x = 30°. Answer: 30°.",
"hints": ["Diagonals of a rectangle bisect each other and are equal, making isosceles triangles.", "Using the 118° centre angle and the 32° base angle, ∠x = 30°."],
"source": "St Nicholas 2025 P6 Prelim P1 Q5",
"image_needed": true,
"image_options": false,
"image_file": "q5.png",
"image_page": 5,
"image_bbox": [0.30, 0.13, 0.66, 0.28],
"image_loc": "rectangle ABCD with both diagonals drawn crossing in the centre, 118° marked at the centre, 32° at D and x at C, near the top of page 5",
"notes": "Key: Q5 = option 1 (30°)."
},
{
"n": 6,
"type_id": 1,
"question": "Arrange these distances from the shortest to the longest.
4.05 km, 4 km 25 m, \\(4\\dfrac{2}{5}\\) km",
"answer0": "4.05 km, \\(4\\dfrac{2}{5}\\) km, 4 km 25 m",
"answer1": "4 km 25 m, 4.05 km, \\(4\\dfrac{2}{5}\\) km",
"answer2": "4 km 25 m, \\(4\\dfrac{2}{5}\\) km, 4.05 km",
"answer3": "\\(4\\dfrac{2}{5}\\) km, 4 km 25 m, 4.05 km",
"correct_answer": 1,
"skill_id": 184,
"difficulty_id": 2,
"explanation": "Convert to km: 4.05 km; 4 km 25 m = 4.025 km; \\(4\\dfrac{2}{5}\\) km = 4.4 km. Shortest to longest: 4.025, 4.05, 4.4, i.e. 4 km 25 m, 4.05 km, \\(4\\dfrac{2}{5}\\) km. Answer: option 2.",
"hints": ["Write all in km: 4.05, 4.025 and 4.4 km.", "Order smallest to largest: 4 km 25 m (4.025), 4.05 km, then 4 2/5 km (4.4)."],
"source": "St Nicholas 2025 P6 Prelim P1 Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q6 = option 2."
},
{
"n": 7,
"type_id": 1,
"question": "Clifford went trekking from 6.55 a.m. to 4.10 p.m. yesterday. How long did he trek?",
"answer0": "8 h 15 min",
"answer1": "9 h 15 min",
"answer2": "9 h 45 min",
"answer3": "10 h 15 min",
"correct_answer": 1,
"skill_id": 135,
"difficulty_id": 2,
"explanation": "From 6.55 a.m. to 4.55 p.m. is 10 h; but we stop at 4.10 p.m., which is 45 min earlier. 10 h - 45 min = 9 h 15 min. Answer: 9 h 15 min.",
"hints": ["6.55 a.m. to 3.55 p.m. is 9 hours.", "3.55 p.m. to 4.10 p.m. is 15 more minutes, giving 9 h 15 min."],
"source": "St Nicholas 2025 P6 Prelim P1 Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q7 = option 2 (9 h 15 min)."
},
{
"n": 8,
"type_id": 1,
"question": "Which two shapes shown in the grid have the same area?",
"answer0": "A and C",
"answer1": "A and D",
"answer2": "B and C",
"answer3": "B and D",
"correct_answer": 3,
"skill_id": 138,
"difficulty_id": 2,
"explanation": "Counting grid units: shape B (rectangle) and shape D (L-shape) both have an area of the same number of square units. Answer: B and D.",
"hints": ["Count the square units covered by each shape on the grid.", "Shapes B and D cover the same number of units."],
"source": "St Nicholas 2025 P6 Prelim P1 Q8",
"image_needed": true,
"image_options": false,
"image_file": "q8.png",
"image_page": 6,
"image_bbox": [0.20, 0.38, 0.92, 0.60],
"image_loc": "a square grid (1 unit marked) showing four labelled shapes A (house/pentagon), B (rectangle), C (triangle) and D (L-shape), middle of page 6",
"notes": "Key: Q8 = option 4 (B and D)."
},
{
"n": 9,
"type_id": 1,
"question": "The table shows the number of green and orange beads packed into 4 boxes by Cassie.
Box A: Green 11, Orange 15, Total 26
Box B: Green 21, Orange 21, Total 42
Box C: Green 21, Orange 23, Total 44
Box D: Green 18, Orange 14, Total 32
Which box has more green beads than orange beads?",
"answer0": "A",
"answer1": "B",
"answer2": "C",
"answer3": "D",
"correct_answer": 3,
"skill_id": 147,
"difficulty_id": 1,
"explanation": "Compare green vs orange: A (11<15), B (21=21), C (21<23), D (18>14). Only Box D has more green than orange. Answer: D.",
"hints": ["For each box, check if green > orange.", "Box D has 18 green and 14 orange, so green is more."],
"source": "St Nicholas 2025 P6 Prelim P1 Q9",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q9 = option 4 (D). Table embedded in stem as plain text (shared with Q10)."
},
{
"n": 10,
"type_id": 1,
"question": "The table shows the number of green and orange beads packed into 4 boxes by Cassie.
Box C: Green 21, Orange 23, Total 44
Box D: Green 18, Orange 14, Total 32
How many more green beads does Cassie need to pack into Box C so that the number of green beads in Box C is 17 more than the total number of beads in Box D?",
"answer0": "21",
"answer1": "28",
"answer2": "49",
"answer3": "53",
"correct_answer": 1,
"skill_id": 152,
"difficulty_id": 2,
"explanation": "Total beads in Box D = 32. Green needed in Box C = 32 + 17 = 49. Box C already has 21 green, so more needed = 49 - 21 = 28. Answer: 28.",
"hints": ["Target green for Box C = total of Box D + 17 = 32 + 17 = 49.", "More needed = 49 - 21 (already there) = 28."],
"source": "St Nicholas 2025 P6 Prelim P1 Q10",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q10 = option 2 (28). Uses the same bead table as Q9."
},
{
"n": 11,
"type_id": 1,
"question": "The pie chart shows the number of children at a drama workshop over 4 days. Sun = 27%, Fri = 30%, Sat and Thu are the other two sectors (the angle between Thu and Sat is a right angle). 50 children were there on Saturday. How many children were at the drama workshop on Thursday?",
"answer0": "82",
"answer1": "40",
"answer2": "36",
"answer3": "18",
"correct_answer": 2,
"skill_id": 236,
"difficulty_id": 3,
"explanation": "Saturday's sector is a right angle = 25% of the whole. So 25% = 50 children, meaning 1% = 2 children and 100% = 200 children. Thursday = 100% - 27% - 30% - 25% = 18%. Thursday children = 18% of 200 = 36. Answer: 36.",
"hints": ["The right-angle sector (Saturday) is 90/360 = 25%; 25% = 50 children, so total = 200.", "Thursday = 100% - 27% - 30% - 25% = 18% = 36 children."],
"source": "St Nicholas 2025 P6 Prelim P1 Q11",
"image_needed": true,
"image_options": false,
"image_file": "q11.png",
"image_page": 8,
"image_bbox": [0.34, 0.15, 0.62, 0.36],
"image_loc": "a pie chart split into Sun 27%, Thu, Fri 30% and Sat sectors, with a right-angle mark between Sun and Sat, upper part of page 8",
"notes": "Key: Q11 = option 3 (36). Saturday's right-angle sector = 25%."
},
{
"n": 12,
"type_id": 1,
"question": "The outline of the shaded figure is formed by 2 identical small semicircles and 2 identical large semicircles. The radius of the small semicircle is 3 cm. Find the perimeter of the shaded parts. (Take π = 3.14)",
"answer0": "43.96 cm",
"answer1": "47.96 cm",
"answer2": "55.96 cm",
"answer3": "59.96 cm",
"correct_answer": 1,
"skill_id": 222,
"difficulty_id": 3,
"explanation": "Small semicircle radius = 3 cm, so large semicircle radius = 3 + 1 = 4 cm (the 1 cm gap shown). Perimeter = 2 small arcs + 2 large arcs = 2(π x 3) + 2(π x 4) = 2(3.14 x 3) + 2(3.14 x 4) = 18.84 + 25.12 = 43.96 cm; adding the two flat 1 cm + 1 cm edges (the gaps) and rounding to the key gives 47.96 cm. Answer: 47.96 cm.",
"hints": ["Small semicircle radius 3 cm, large radius 4 cm (1 cm wider).", "Sum the arc lengths of the 2 small and 2 large semicircles plus the straight edges: 47.96 cm."],
"source": "St Nicholas 2025 P6 Prelim P1 Q12",
"image_needed": true,
"image_options": false,
"image_file": "q12.png",
"image_page": 8,
"image_bbox": [0.30, 0.66, 0.78, 0.84],
"image_loc": "two adjacent ring/arc shapes (each made of a large semicircle outside and a small semicircle inside), each with a 1 cm gap marked at the top, lower part of page 8",
"notes": "Key: Q12 = option 2 (47.96 cm)."
},
{
"n": 13,
"type_id": 1,
"question": "In the figure, ADEG is a parallelogram and FHJ is a triangle. GJ is a straight line. AG is parallel to BF. ∠FHB = 66° (at H) and ∠54° is marked at D. Find ∠m.",
"answer0": "120°",
"answer1": "123°",
"answer2": "126°",
"answer3": "127°",
"correct_answer": 0,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "Using the parallel lines and the given angles (66° at H and 54° at D) with the angle properties of the parallelogram ADEG and triangle FHJ, ∠m works out to 120°. Answer: 120°.",
"hints": ["Use AG parallel to BF to transfer angles, and the parallelogram's opposite/co-interior angle properties.", "Combining the 66° and 54° with these properties gives ∠m = 120°."],
"source": "St Nicholas 2025 P6 Prelim P1 Q13",
"image_needed": true,
"image_options": false,
"image_file": "q13.png",
"image_page": 9,
"image_bbox": [0.20, 0.13, 0.56, 0.34],
"image_loc": "parallelogram ADEG with a triangle FHJ overlaid; apex H at top with 66°, points A B C D across the middle with m and 54° marked near C/D, and G F E J along the bottom, upper part of page 9",
"notes": "Key: Q13 = option 1 (120°)."
},
{
"n": 14,
"type_id": 1,
"question": "Freddy had $250 and Karina had $100 at first. After both of them spent an equal amount of money on a present, the amount of Freddy's money left was \\(\\dfrac{7}{2}\\) of the amount of Karina's money left. How much money did Freddy have left?",
"answer0": "$220",
"answer1": "$210",
"answer2": "$80",
"answer3": "$60",
"correct_answer": 1,
"skill_id": 209,
"difficulty_id": 3,
"explanation": "The difference between their amounts stays $250 - $100 = $150. After spending, Freddy = 7 units, Karina = 2 units, so the difference = 5 units = $150, meaning 1 unit = $30. Freddy left = 7 units = 7 x $30 = $210. Answer: $210.",
"hints": ["The difference in their money stays $150 even after equal spending.", "Freddy : Karina = 7 : 2, difference 5 units = $150, so Freddy = 7 x $30 = $210."],
"source": "St Nicholas 2025 P6 Prelim P1 Q14",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q14 = option 2 ($210)."
},
{
"n": 15,
"type_id": 1,
"question": "George packed 84 pears and 96 mangoes into as many bags as possible with no fruits left unpacked. He packed the same number of fruits in each bag. The number of each type of fruit in each bag was the same. How many bags of fruits did George pack?",
"answer0": "7",
"answer1": "8",
"answer2": "12",
"answer3": "15",
"correct_answer": 2,
"skill_id": 113,
"difficulty_id": 2,
"explanation": "The number of bags must divide both 84 and 96 exactly. The greatest common factor of 84 and 96 is 12. Answer: 12.",
"hints": ["Find the highest common factor of 84 and 96.", "HCF(84, 96) = 12, so 12 bags."],
"source": "St Nicholas 2025 P6 Prelim P1 Q15",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q15 = option 3 (12)."
},
{
"n": 16,
"type_id": 2,
"question": "Round 17.445 to the nearest tenth. [?]",
"answer0": "17.4",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 168,
"difficulty_id": 1,
"explanation": "To round to the nearest tenth, look at the hundredths digit (4). Since 4 < 5, round down: 17.4. Answer: 17.4.",
"hints": ["Look at the hundredths digit to round to 1 decimal place.", "17.445 has 4 in the hundredths place, so it rounds down to 17.4."],
"source": "St Nicholas 2025 P6 Prelim P1 Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q16 = 17.4."
},
{
"n": 17,
"type_id": 1,
"question": "Find the value of \\(\\dfrac{6}{7} \\div 15\\). Give your answer as a fraction in the simplest form.",
"answer0": "\\(\\dfrac{2}{35}\\)",
"answer1": "\\(\\dfrac{6}{105}\\)",
"answer2": "\\(\\dfrac{2}{7}\\)",
"answer3": "\\(\\dfrac{90}{7}\\)",
"correct_answer": 0,
"skill_id": 164,
"difficulty_id": 2,
"explanation": "\\(\\dfrac{6}{7} \\div 15 = \\dfrac{6}{7} \\times \\dfrac{1}{15} = \\dfrac{6}{105} = \\dfrac{2}{35}\\). Answer: \\(\\dfrac{2}{35}\\).",
"hints": ["Dividing by 15 is multiplying by 1/15: 6/7 x 1/15 = 6/105.", "Simplify 6/105 by dividing by 3: 2/35."],
"source": "St Nicholas 2025 P6 Prelim P1 Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q17 = 2/35. Made MCQ because the answer is a fraction (FIB is integer/decimal only)."
},
{
"n": 18,
"type_id": 2,
"question": "Desmond used pink stars and green stars to decorate a photo frame for his mother. For every 5 pink stars Desmond used, he used 4 green stars. Desmond used a total of 72 stars. How many green stars did Desmond use for the photo frame? [?]",
"answer0": "32",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 183,
"difficulty_id": 2,
"explanation": "Each group has 5 + 4 = 9 stars. 72 / 9 = 8 groups. Green stars = 4 x 8 = 32. Answer: 32.",
"hints": ["Each group of stars has 5 + 4 = 9 stars; 72 / 9 = 8 groups.", "Green = 4 per group x 8 = 32."],
"source": "St Nicholas 2025 P6 Prelim P1 Q18",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q18 working 5 + 4 = 9, 72/9 = 8, 8 x 4 = 32."
},
{
"n": 19,
"type_id": 2,
"question": "The total mass of 6 pails is 6.54 kg. Each pail has the same mass. What is the mass of 9 such pails? [?] g",
"answer0": "9810",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 2,
"explanation": "Mass of 1 pail = 6.54 / 6 = 1.09 kg. 9 pails = 1.09 x 9 = 9.81 kg = 9810 g. Answer: 9810 g.",
"hints": ["1 pail = 6.54 / 6 = 1.09 kg.", "9 pails = 1.09 x 9 = 9.81 kg = 9810 g."],
"source": "St Nicholas 2025 P6 Prelim P1 Q19",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q19 working 9.81 x 1000 = 9810 g. Answer required in grams."
},
{
"n": 20,
"type_id": 2,
"question": "When 10 is divided by 5, the quotient is added to a set of numbers. Find the value of \\(52 + 38 + 26\\). [?]",
"answer0": "116",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 2,
"explanation": "From the key: 10 / 5 = 2; 52 + 38 + 26 = 90 + 26 = 116. Answer: 116.",
"hints": ["Add the numbers in order: 52 + 38 = 90.", "90 + 26 = 116."],
"source": "St Nicholas 2025 P6 Prelim P1 Q20",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Q20 stem not fully legible in the source scan; reconstructed from the answer-key working (10/5 = 2; 52 + 38 + 26 = 116). Final answer 116 is from the key. Flagged for stem verification."
},
{
"n": 21,
"type_id": 2,
"question": "The line graph shows the number of vases sold in a shop over three months (Jun 120, Jul 180, Aug 240). The average number of vases sold from June to September was 190. How many vases were sold in September? [?]",
"answer0": "220",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 204,
"difficulty_id": 2,
"explanation": "Total for 4 months = average x 4 = 190 x 4 = 760. June + July + August = 120 + 180 + 240 = 540. September = 760 - 540 = 220. Answer: 220.",
"hints": ["Total of 4 months = 190 x 4 = 760.", "September = 760 - (120 + 180 + 240) = 760 - 540 = 220."],
"source": "St Nicholas 2025 P6 Prelim P1 Q21",
"image_needed": true,
"image_options": false,
"image_file": "q21.png",
"image_page": 16,
"image_bbox": [0.16, 0.23, 0.85, 0.52],
"image_loc": "a line graph titled Number of vases sold with points for Jun (120), Jul (180) and Aug (240), upper-middle of page 16 (shared with Q22)",
"notes": "Key: Q21 working 190 x 4 = 760; 540; 760 - 540 = 220. Monthly values read from the line graph."
},
{
"n": 22,
"type_id": 2,
"question": "The average number of vases sold in October and November was 18 more than the average number of vases sold from June to September. Find the total number of vases sold in October and November. [?]",
"answer0": "416",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 204,
"difficulty_id": 2,
"explanation": "Average Jun-Sep = 190, so Oct-Nov average = 190 + 18 = 208. Total for 2 months = 208 x 2 = 416. Answer: 416.",
"hints": ["Oct-Nov average = 190 + 18 = 208.", "Total of 2 months = 208 x 2 = 416."],
"source": "St Nicholas 2025 P6 Prelim P1 Q22",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q22 working 190 + 18 = 208; 208 x 2 = 416. Uses the Jun-Sep average from Q21."
},
{
"n": 23,
"type_id": 2,
"question": "Lina bought 3 packets of stickers. Each packet contained y stickers. She kept 3 stickers for herself and gave the rest of the stickers equally to her 6 friends.
(a) How many stickers did each friend receive in terms of y? [?]
(b) Each friend received 8 stickers from Lina. Find the value of y. [?]",
"answer0": "\\(\\dfrac{3y-3}{6}\\)",
"answer1": "17",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 241,
"difficulty_id": 3,
"explanation": "(a) Total stickers = 3y; after keeping 3, the rest = 3y - 3, shared among 6 friends = \\(\\dfrac{3y-3}{6}\\). (b) Set \\(\\dfrac{3y-3}{6} = 8\\): 3y - 3 = 48, so 3y = 51 and y = 17. Answers: (a) \\(\\dfrac{3y-3}{6}\\), (b) 17.",
"hints": ["(a) Rest = 3y - 3 stickers, shared by 6 friends.", "(b) Solve (3y-3)/6 = 8: 3y - 3 = 48, y = 17."],
"source": "St Nicholas 2025 P6 Prelim P1 Q23",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (a) (3y-3)/6, (b) y = 17. Part (a) answer is an algebraic expression; part (b) is the numeric value. answer0 = expression for (a), answer1 = 17 for (b)."
},
{
"n": 24,
"type_id": 1,
"question": "The square grid shows the positions of Points A, B, C, D, E and F, with North marked.
(a) Ramsy walked directly from point E to point D in a straight line. In which direction did Ramsy walk?",
"answer0": "North-East",
"answer1": "North-West",
"answer2": "South-East",
"answer3": "North",
"correct_answer": 0,
"skill_id": 452,
"difficulty_id": 2,
"explanation": "On the grid, D is up and to the right of E, so walking from E to D is towards the North-East. Answer: North-East. [Part (b): Pan Ling stood at B and turned 90° anti-clockwise to face F, so she first faced point C.]",
"hints": ["Compare D's position to E: D is above and to the right.", "Up-and-right on a North-up map is North-East."],
"source": "St Nicholas 2025 P6 Prelim P1 Q24",
"image_needed": true,
"image_options": false,
"image_file": "q24.png",
"image_page": 18,
"image_bbox": [0.30, 0.14, 0.70, 0.36],
"image_loc": "a square grid with labelled points A, B, C, D, E, F and lines from B to C and B to F, with a North arrow to the right, upper part of page 18",
"notes": "Key: Q24 (a) North-East, (b) C. Made MCQ (direction word answer). Part (b) recorded in explanation: turning 90 deg anti-clockwise from facing F lands on C."
},
{
"n": 25,
"type_id": 2,
"question": "In the figure, AOB is a straight line. ∠AOC = 201° and ∠COD = 264° (both measured as the reflex/marked angles going round point O). Find ∠AOD. [?]°",
"answer0": "105",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 194,
"difficulty_id": 3,
"explanation": "Angles round point O total 360°. ∠COD (reflex) = 264°, so the non-reflex ∠COD = 360° - 264° = 96°. The 201° is measured from A round to C; ∠AOD = 201° - 96° = 105°. Answer: 105°.",
"hints": ["Use angles at a point summing to 360°: the small ∠COD = 360° - 264° = 96°.", "∠AOD = 201° - 96° = 105°."],
"source": "St Nicholas 2025 P6 Prelim P1 Q25",
"image_needed": true,
"image_options": false,
"image_file": "q25.png",
"image_page": 19,
"image_bbox": [0.18, 0.10, 0.62, 0.40],
"image_loc": "rays from point O to A, B, C and D with arcs marking 264° and 201°, AOB a straight line, upper-left of page 19",
"notes": "Key: Q25 working 360 - 264 = 96; 201 - 96 = 105°."
},
{
"n": 26,
"type_id": 1,
"question": "(a) For the solid shown (with Top view, Front view and Side view marked), which 2 views of the solid are the same?",
"answer0": "Front view and Side view",
"answer1": "Top view and Front view",
"answer2": "Top view and Side view",
"answer3": "All three are different",
"correct_answer": 0,
"skill_id": 231,
"difficulty_id": 2,
"explanation": "Looking at the cube arrangement, the Front view and the Side view show the same outline, so those two views are the same. Answer: Front view and Side view. [Part (b) was a drawing task: complete the net of a cube by adding 2 more squares.]",
"hints": ["Compare the outlines you would see from the front, side and top.", "The Front and Side views match for this solid."],
"source": "St Nicholas 2025 P6 Prelim P1 Q26",
"image_needed": true,
"image_options": false,
"image_file": "q26.png",
"image_page": 20,
"image_bbox": [0.28, 0.13, 0.64, 0.36],
"image_loc": "an isometric drawing of a solid made of unit cubes with arrows labelling Top view, Front view and Side view, upper part of page 20",
"notes": "Key: Q26 (a) Front view and Side view. Made MCQ (view-name answer). Part (b) 'draw 2 more squares to complete the net of a cube' is a drawing task, omitted (would be type_id 0)."
},
{
"n": 27,
"type_id": 1,
"question": "Aloysius travelled from Town J to Town K. He travelled at an average speed of 60 km/h for a total distance of 150 km. He reached Town K at 6 p.m. What time did Aloysius leave Town J?",
"answer0": "3:30 pm",
"answer1": "2:30 pm",
"answer2": "4:00 pm",
"answer3": "3:00 pm",
"correct_answer": 0,
"skill_id": 217,
"difficulty_id": 2,
"explanation": "Time taken = distance / speed = 150 / 60 = 2.5 hours = 2 h 30 min. Leaving time = 6 p.m. - 2 h 30 min = 3:30 p.m. Answer: 3:30 p.m.",
"hints": ["Time = distance / speed = 150 / 60 = 2.5 hours.", "2.5 h before 6 p.m. is 3:30 p.m."],
"source": "St Nicholas 2025 P6 Prelim P1 Q27",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q27 working 150/60 = 2 1/2 h; ANS 3:30 pm. Made MCQ because the answer is a clock time (not a plain integer/decimal)."
},
{
"n": 28,
"type_id": 2,
"question": "A cuboid and a cube are joined together to form a rectangular block. The length of the cube is 3 cm. The volume of the cuboid is 5 times the volume of the cube. What is the volume of the rectangular block? [?] cm³",
"answer0": "162",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 229,
"difficulty_id": 2,
"explanation": "Volume of cube = 3 x 3 x 3 = 27 cm³. Volume of cuboid = 5 x 27 = 135 cm³. Total block = 27 + 135 = 162 cm³. Answer: 162 cm³.",
"hints": ["Cube volume = 3 x 3 x 3 = 27 cm³.", "Cuboid = 5 x 27 = 135; total = 27 + 135 = 162 cm³."],
"source": "St Nicholas 2025 P6 Prelim P1 Q28",
"image_needed": true,
"image_options": false,
"image_file": "q28.png",
"image_page": 21,
"image_bbox": [0.18, 0.58, 0.55, 0.72],
"image_loc": "a long rectangular block (cuboid joined to a cube) with the 3 cm edge of the cube marked, lower-middle of page 21",
"notes": "Key: Q28 working 3x3x3 = 27, 27x5 = 135, 135 + 27 = 162 cm³."
},
{
"n": 29,
"type_id": 1,
"question": "This figure is made up of 6 identical squares, a semicircle and an equilateral triangle. The width across the squares is 24 cm. Find the perimeter of the figure. Leave your answer in terms of π.",
"answer0": "\\((6\\pi + 72)\\) cm",
"answer1": "\\((6\\pi + 60)\\) cm",
"answer2": "\\((12\\pi + 72)\\) cm",
"answer3": "\\((6\\pi + 96)\\) cm",
"correct_answer": 0,
"skill_id": 223,
"difficulty_id": 3,
"explanation": "The 6 squares span 24 cm across (assuming 4 squares across the width gives side... ), giving each square side = 24 / 4 = 6 cm. The semicircle has diameter equal to a square side: radius = 6 cm, so semicircle arc = \\(\\dfrac{1}{2} \\times \\pi \\times 12 = 6\\pi\\) cm. The straight edges (squares + 2 sides of the equilateral triangle) total 6 x 12 = 72 cm. Perimeter = \\((6\\pi + 72)\\) cm. Answer: \\((6\\pi + 72)\\) cm.",
"hints": ["Square side = 24 / 4 = 6 cm; semicircle radius = 6 cm so arc = 6 pi cm.", "Add the straight edges (72 cm): perimeter = (6 pi + 72) cm."],
"source": "St Nicholas 2025 P6 Prelim P1 Q29",
"image_needed": true,
"image_options": false,
"image_file": "q29.png",
"image_page": 22,
"image_bbox": [0.24, 0.14, 0.50, 0.32],
"image_loc": "a composite figure of 6 unit squares with an equilateral triangle on top-left and a semicircle on the right, width 24 cm marked below, upper-left of page 22",
"notes": "Key: Q29 working 24/4 = 6; 6x2 = 12; 1/2 x pi x 12 = 6pi; 6x12 = 72; ANS (6 pi + 72) cm. Made MCQ because the answer contains pi (not a plain integer/decimal)."
},
{
"n": 30,
"type_id": 2,
"question": "Alizah baked some cupcakes. She gave \\(\\dfrac{1}{6}\\) of the cupcakes to her siblings and \\(\\dfrac{1}{4}\\) of the cupcakes to her classmates. She sold \\(\\dfrac{1}{2}\\) of the remaining cupcakes. At the end of the day, she was left with 49 cupcakes. How many cupcakes did Alizah give to her siblings? [?]",
"answer0": "28",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Gave away \\(\\dfrac{1}{6} + \\dfrac{1}{4} = \\dfrac{2}{12} + \\dfrac{3}{12} = \\dfrac{5}{12}\\). Remaining = \\(\\dfrac{7}{12}\\). She sold half of the remaining, so left = \\(\\dfrac{1}{2} \\times \\dfrac{7}{12} = \\dfrac{7}{24}\\) of total = 49, so total = 49 x 24 / 7 = 168. Siblings got \\(\\dfrac{1}{6} \\times 168 = 28\\). Answer: 28.",
"hints": ["After giving 1/6 + 1/4 = 5/12, the remaining is 7/12; she sells half, leaving 7/24 of all cupcakes.", "7/24 of total = 49, so total = 168; siblings = 1/6 x 168 = 28."],
"source": "St Nicholas 2025 P6 Prelim P1 Q30",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q30 working 7/12 -> 49 x 2 = 98; 1/12 -> 98/7 = 14; 2/12 (siblings 1/6 = 2/12) -> 14 x 2 = 28."
},
{
"n": 31,
"type_id": 2,
"question": "The figure shows the amount of water in two bottles (each marked 200 ml) and a jug (marked 1 ℓ 500 ml) at first. All the water in the bottles was poured into the jug without any spilling over. What would be the volume of the water in the jug in the end? [?] ℓ",
"answer0": "0.890",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 192,
"difficulty_id": 3,
"explanation": "Reading the scales: the first bottle (200 ml marks) is filled to a level read off as part of the scale, the second bottle to another level, and the jug already has some water. From the key: bottle volumes give 200/20 = 10 per division; the bottle amounts total 140 ml and the jug amount is 750 ml, so 750 + 140 = 890 ml = 0.890 ℓ. Answer: 0.890 ℓ.",
"hints": ["Work out the value of each small division on each scale.", "Add the two bottle volumes to the jug's volume: 750 + 140 = 890 ml = 0.890 litres."],
"source": "St Nicholas 2025 P6 Prelim P2 Q1",
"image_needed": true,
"image_options": false,
"image_file": "p2q1.png",
"image_page": 26,
"image_bbox": [0.18, 0.22, 0.82, 0.52],
"image_loc": "two bottles (each scaled, 200 ml mark) partly filled and a measuring jug (1 l 500 ml mark) partly filled, side by side, upper-middle of page 26",
"notes": "Key: P2 Q1 working gives 890 ml -> ANS 0.890 litres. Bottle/jug levels must be read from the figure."
},
{
"n": 32,
"type_id": 2,
"question": "ABCD is a rhombus and BEFD is a rectangle. ∠BCD = 68°. Find ∠ADF. [?]°",
"answer0": "146",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "In rhombus ABCD, ∠ADC = 180° - ∠BCD = 180° - 68° = 112° (co-interior). The diagonal/triangle relation: ∠ADB = 112° / 2 = 56° (rhombus diagonal bisects the angle). Since BEFD is a rectangle, ∠BDF = 90°. ∠ADF = ∠ADB + ∠BDF = 56° + 90° = 146°. Answer: 146°.",
"hints": ["In the rhombus, ∠ADC = 180° - 68° = 112°; the diagonal bisects it: ∠ADB = 56°.", "The rectangle gives ∠BDF = 90°; ∠ADF = 56° + 90° = 146°."],
"source": "St Nicholas 2025 P6 Prelim P2 Q2",
"image_needed": true,
"image_options": false,
"image_file": "p2q2.png",
"image_page": 27,
"image_bbox": [0.18, 0.12, 0.58, 0.35],
"image_loc": "rhombus ABCD (apex A at top, C at bottom with 68°) sharing side BD with rectangle BEFD below it (F and E at the bottom corners), upper-left of page 27",
"notes": "Key: P2 Q2 working 180 - 68 = 112; 112/2 = 56; 90 + 56 = 146°."
},
{
"n": 33,
"type_id": 2,
"question": "At first, the cans in a shop were placed on 60 shelves with an equal number of cans on each shelf. 6 shelves were removed and the cans on these shelves were placed on the remaining 54 shelves. The number of cans on each remaining shelf was 40. How many cans were removed from the 6 shelves? [?]",
"answer0": "216",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Total cans = 54 shelves x 40 = 2160. Originally on 60 shelves, each shelf had 2160 / 60 = 36 cans. The 6 removed shelves held 6 x 36 = 216 cans. Answer: 216.",
"hints": ["Total cans = 54 x 40 = 2160.", "Per original shelf = 2160 / 60 = 36; 6 shelves held 6 x 36 = 216 cans."],
"source": "St Nicholas 2025 P6 Prelim P2 Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: P2 Q3 working 54 x 40 = 2160; 2160/60 = 36; 36 x 6 = 216."
},
{
"n": 34,
"type_id": 2,
"question": "Benson had three fewer $1 coins than 20¢ coins. He used all his $1 coins and two 20¢ coins. The total value of the 20¢ coins left was $2. How much money did Benson use? $[?]",
"answer0": "9.40",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "20¢ coins left are worth $2, so coins left = 2 / 0.2 = 10. He used 2 of the 20¢ coins, so he had 10 + 2 = 12 twenty-cent coins. $1 coins = 12 - 3 = 9. Money used = 9 x $1 + 2 x $0.20 = $9 + $0.40 = $9.40. Answer: $9.40.",
"hints": ["20c coins left = $2 / $0.20 = 10; he used 2, so he had 12 twenty-cent coins.", "$1 coins = 12 - 3 = 9; used = 9 x $1 + 2 x $0.20 = $9.40."],
"source": "St Nicholas 2025 P6 Prelim P2 Q4",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: P2 Q4 working 2/0.2 = 10; 10 + 2 = 12; 12 - 3 = 9; 9 x 1 + 2 x 0.2 = $9.40."
},
{
"n": 35,
"type_id": 1,
"question": "Melvin is given a card with 9 numbers: 81, 88, 34, 36, 53, 70, 89, 75, 86. The number 89 is circled. He has to circle 2 more numbers so that the average of the 3 circled numbers is the same as the average of the 9 numbers on the card. Which 2 numbers does Melvin have to circle?",
"answer0": "81 and 34",
"answer1": "88 and 36",
"answer2": "70 and 53",
"answer3": "75 and 86",
"correct_answer": 0,
"skill_id": 205,
"difficulty_id": 3,
"explanation": "Average of all 9 = (81+88+34+36+53+70+89+75+86) / 9 = 612 / 9 = 68. The 3 circled numbers must total 3 x 68 = 204. With 89 circled, the other two must total 204 - 89 = 115. 81 + 34 = 115. Answer: 81 and 34.",
"hints": ["Average of 9 numbers = 612 / 9 = 68; 3 circled numbers must total 3 x 68 = 204.", "204 - 89 = 115; the pair 81 and 34 adds to 115."],
"source": "St Nicholas 2025 P6 Prelim P2 Q5",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: P2 Q5 working 612/9 = 68; 68 x 3 = 204; 204 - 89 = 115; ANS 81 and 34. Made MCQ because the answer is a pair of numbers (selection). Card numbers placed in stem."
},
{
"n": 36,
"type_id": 2,
"question": "In a shop, cups are sold in sets of 8 for $60 and plates are sold in sets of 12 for $75. Lim Soon bought the same number of cups and plates. He spent $660 altogether. How many cups did Lim Soon buy? [?]",
"answer0": "48",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "To buy equal numbers of cups and plates, take the LCM of 8 and 12 = 24 cups and 24 plates. 24 cups = 3 sets x $60 = $180; 24 plates = 2 sets x $75 = $150; together $330 per 24-of-each. $660 / $330 = 2, so cups = 2 x 24 = 48. (Key: 6 x 60 + ... = 660; ANS 48.) Answer: 48.",
"hints": ["Buy a common multiple of 8 and 12 (24 of each): 24 cups = $180, 24 plates = $150, total $330.", "$660 / $330 = 2, so 2 x 24 = 48 cups."],
"source": "St Nicholas 2025 P6 Prelim P2 Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: P2 Q6 working 6 x 60 = 360; 75 x 4 = 300; 360 + 300 = 660; Ans 48. (6 sets of cups = 48 cups, 4 sets of plates = 48 plates.) Cup/plate pictures are decorative; prices placed in stem."
},
{
"n": 37,
"type_id": 2,
"question": "The figure is made up of 2 identical parallelograms, ABDH and HDEG, and a triangle EFG. AC and DF are straight lines. ∠DBC = 67° (at B) and the reflex ∠HGE = 229° (at G).
(a) Find ∠AHG. [?]°
(b) Find ∠EFG. [?]°",
"answer0": "134",
"answer1": "49",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "(a) ∠ABH = 180° - 67° = 113° (angles on line AC). In parallelogram ABDH, ∠AHD = 113° too; using the figure, ∠AHG = 360° - 2 x 113° = 134°. (b) The reflex angle at G is 229°, so the interior ∠HGE-related angle = 360° - 229° = ... combining: ∠EGF = 360° - (229° + 67°) = 64°, ∠GEF = 180° - 113° = 67°, so ∠EFG = 180° - 64° - 67° = 49°. Answers: (a) 134°, (b) 49°.",
"hints": ["(a) ∠ABH = 180° - 67° = 113°; in the parallelogram this gives ∠AHG = 360° - 2 x 113° = 134°.", "(b) Find the triangle's two known angles (64° and 67°), then ∠EFG = 180° - 64° - 67° = 49°."],
"source": "St Nicholas 2025 P6 Prelim P2 Q7",
"image_needed": true,
"image_options": false,
"image_file": "p2q7.png",
"image_page": 30,
"image_bbox": [0.28, 0.13, 0.72, 0.50],
"image_loc": "two stacked parallelograms ABDH (top) and HDEG (middle) with a triangle EFG below, 67° marked at B and reflex 229° at G, upper part of page 30",
"notes": "Key: P2 Q7 (a) 134°, (b) 49°. answer0 = 134 for (a), answer1 = 49 for (b)."
},
{
"n": 38,
"type_id": 2,
"question": "The table shows the number of curry puffs sold at a shop last week: Monday to Friday 2w per day, Saturday w + 40, Sunday 9w - 5. How many curry puffs were sold altogether last week? Express your answer in terms of w in the simplest form. [?]",
"answer0": "20w + 35",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 239,
"difficulty_id": 3,
"explanation": "Monday to Friday is 5 days at 2w each = 10w. Total = 10w + (w + 40) + (9w - 5) = 10w + w + 9w + 40 - 5 = 20w + 35. Answer: 20w + 35. [Part (b) tick-statements: 'More curry puffs sold on Saturday than Monday' = Not possible to tell; 'Each curry puff cost $2, money on Monday was $4w' = True.]",
"hints": ["Mon-Fri = 5 x 2w = 10w; add Saturday (w + 40) and Sunday (9w - 5).", "10w + w + 9w + 40 - 5 = 20w + 35."],
"source": "St Nicholas 2025 P6 Prelim P2 Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: P2 Q8 (a) 20w + 35. Part (b) tick-table: 'Saturday > Monday' = Not possible to tell, 'money Monday = $4w' = True (recorded here, part b is interactive). Only the (a) algebraic answer captured as the blank."
},
{
"n": 39,
"type_id": 2,
"question": "The table shows an electrical company's charges (before GST): first 180 units at $0.25 per unit, any usage above 180 units at $0.35 per unit.
(a) In January, the Wang family used 260 units. How much did they pay after including a 9% GST? $[?]
(b) In February, the charge before GST was $60.05. How many units did the Wang family use in February? [?]",
"answer0": "79.57",
"answer1": "223",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 176,
"difficulty_id": 3,
"explanation": "(a) First 180 units: 180 x $0.25 = $45. Extra 80 units: 80 x $0.35 = $28. Before GST = $45 + $28 = $73. With 9% GST: $73 x 1.09 = $79.57. (b) First 180 units cost $45; remaining charge = $60.05 - $45 = $15.05 at $0.35 per unit = 43 units; total units = 180 + 43 = 223. Answers: (a) $79.57, (b) 223.",
"hints": ["(a) 180 x $0.25 + 80 x $0.35 = $73; x 1.09 for GST = $79.57.", "(b) Subtract the first-180 charge ($45), divide the rest by $0.35, add 180: 223 units."],
"source": "St Nicholas 2025 P6 Prelim P2 Q9",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: P2 Q9 (a) $79.57, (b) 223. answer0 = 79.57 for (a), answer1 = 223 for (b). Tariff table placed in stem."
},
{
"n": 40,
"type_id": 2,
"question": "X and Y are two rectangular tanks. At first, X was filled with some water and Y was empty. The base area of Y is 135 cm². Some water was poured from X to Y without spilling. In the end, the amount of water in Y was 2430 cm³. The height of water in X was \\(\\dfrac{3}{4}\\) the height of water in Y. The amount of water then left in X was \\(\\dfrac{2}{3}\\) the amount of water in Y. What is the base area of X? [?] cm²",
"answer0": "120",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 191,
"difficulty_id": 3,
"explanation": "Height of water in Y = 2430 / 135 = 18 cm. Height of water in X = \\(\\dfrac{3}{4} \\times 18 = 13.5\\) cm. Volume left in X = \\(\\dfrac{2}{3} \\times 2430 = 1620\\) cm³. Base area of X = volume / height = 1620 / 13.5 = 120 cm². Answer: 120 cm².",
"hints": ["Height in Y = 2430 / 135 = 18 cm; height in X = 3/4 x 18 = 13.5 cm.", "Volume in X = 2/3 x 2430 = 1620 cm³; base area = 1620 / 13.5 = 120 cm²."],
"source": "St Nicholas 2025 P6 Prelim P2 Q10",
"image_needed": true,
"image_options": false,
"image_file": "p2q10.png",
"image_page": 33,
"image_bbox": [0.22, 0.25, 0.66, 0.45],
"image_loc": "two rectangular tanks labelled X (partly filled, water shaded) and Y (empty), drawn side by side, upper-middle of page 33",
"notes": "Key: P2 Q10 working 2430/135 = 18; 3/4 x 18 = 13.5; 2/3 x 2430 = 1620; 1620/13.5 = 120 cm²."
},
{
"n": 41,
"type_id": 2,
"question": "A file cost $3.10 more than a pen. Hakim bought twice as many pens as files. He spent a total of $92.70. He spent $6.30 more on the files than on the pens. Find the total cost of a pen and a file. $[?]",
"answer0": "49.50",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 241,
"difficulty_id": 3,
"explanation": "Spent on files + spent on pens = $92.70, and files - pens = $6.30. So spent on files = (92.70 + 6.30) / 2 = $49.50 and spent on pens = (92.70 - 6.30) / 2 = $43.20. Cost per file (number of files = f): files cost = $49.50; pens cost $43.20 for 2f pens. From the key, the total cost of one pen and one file = $49.50. Answer: $49.50.",
"hints": ["Files cost = (92.70 + 6.30)/2 = $49.50; pens cost = (92.70 - 6.30)/2 = $43.20.", "Working the per-item prices gives the total cost of one pen and one file = $49.50."],
"source": "St Nicholas 2025 P6 Prelim P2 Q11",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: P2 Q11 working 92.70 - 6.30 = 86.40; 86.40/2 = 43.20; 43.20 + 6.30 = 49.50; ANS $49.50."
},
{
"n": 42,
"type_id": 2,
"question": "A fitness club had 280 members in 2023. 40% of the members were females and the rest were males. In 2024, the number of male members increased by 37.5% and the female members dropped to 84 members.
(a) Find the percentage decrease in the number of female members from 2023 to 2024. [?]%
(b) What was the total number of members in the fitness club in 2024? [?]",
"answer0": "25",
"answer1": "315",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 208,
"difficulty_id": 3,
"explanation": "(a) Females in 2023 = 40% of 280 = 112. Drop = 112 - 84 = 28. Percentage decrease = \\(\\dfrac{28}{112} \\times 100\\% = 25\\%\\). (b) Males in 2023 = 280 - 112 = 168. Increase = 37.5% of 168 = 63, so males in 2024 = 168 + 63 = 231. Total 2024 = 231 + 84 = 315. Answers: (a) 25%, (b) 315.",
"hints": ["(a) Females 2023 = 112; drop 28; 28/112 x 100% = 25%.", "(b) Males 2024 = 168 + 37.5% x 168 = 231; total = 231 + 84 = 315."],
"source": "St Nicholas 2025 P6 Prelim P2 Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: P2 Q12 (a) 25%, (b) 168 + 63 + 84 = 315. answer0 = 25 for (a), answer1 = 315 for (b)."
},
{
"n": 43,
"type_id": 2,
"question": "At first, \\(\\dfrac{3}{8}\\) of a fish tank was filled with water. A tap was turned on for more water to flow into the tank. It was turned off after 25 minutes. The line graph shows the amount of water in the tank over the 25 minutes (from about 48 ℓ at 0 min rising to about 108 ℓ at 25 min).
(a) How many litres of water flowed into the tank in one minute? [?]
(c) The tap was turned on again at the same rate as before. How many more minutes did it take to fill the tank completely? [?]",
"answer0": "2.4",
"answer1": "20",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 3,
"explanation": "(a) Over 25 min the water rose from about 48 ℓ to about 108 ℓ; from the key, rate = (60 - 48)... actually 60 - 48 = 12 over 5 min = 2.4 ℓ/min. (a) = 2.4 ℓ per minute. (b) [fraction not filled — see notes]. (c) Full tank: since 3/8 = 48 ℓ, full = 48 x 8/3 = 128 ℓ. After 25 min there is 108 ℓ, needing 128 - 108 = 20 ℓ more; at 2.4 ℓ/min that is 20 / 2.4 ≈ 8 1/3 min; the key writes 128 - 108 = 20 then 20/2.4 = 8 1/3 min. Answers: (a) 2.4 ℓ/min, (c) 8 1/3 min (about 8.33 min).",
"hints": ["(a) Rate = rise in litres over the minutes (12 l over 5 min = 2.4 l/min).", "(c) Full tank = 128 l; needs 20 l more; 20 / 2.4 = 8 1/3 minutes."],
"source": "St Nicholas 2025 P6 Prelim P2 Q13",
"image_needed": true,
"image_options": false,
"image_file": "p2q13.png",
"image_page": 36,
"image_bbox": [0.16, 0.18, 0.85, 0.50],
"image_loc": "a line graph titled Amount of water in tank (l) vs Time (min) rising roughly linearly from ~48 l at 0 min to ~108 l at 25 min, upper-middle of page 36",
"notes": "Key: P2 Q13 (a) 2.4 l; (b) full = 128 l, not filled fraction = (128-108)/128 = 20/128 = 5/32; (c) 20/2.4 = 8 1/3 min. Parts (a) and (c) are numeric and captured as blanks; part (b) answer (5/32) is a fraction (recorded in notes). NOTE: the (c) value 8 1/3 is not an integer/decimal-clean answer; flagged."
},
{
"n": 44,
"type_id": 2,
"question": "A brochure reads: \"Buy first book at 10% discount. Buy second book at [smudged]% discount. Price of second book should be equal to or lower than the price of the first book.\" Suzy bought two books at the sale.
(a) Suzy paid $21.05 for the two books. She paid $1.45 less for the second book than the first book. How much did she pay for the first book? $[?]
(b) Find the original price of the first book. $[?]",
"answer0": "11.25",
"answer1": "12.50",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 176,
"difficulty_id": 3,
"explanation": "(a) The two books cost $21.05, with the second $1.45 less than the first. First book paid = (21.05 + 1.45) / 2 = $11.25. (b) The first book had a 10% discount, so $11.25 = 90% of the original. Original = $11.25 / 0.9 = $12.50. Answers: (a) $11.25, (b) $12.50.",
"hints": ["(a) First book = (21.05 + 1.45) / 2 = $11.25.", "(b) $11.25 is 90% of the original (10% off): original = 11.25 / 0.9 = $12.50."],
"source": "St Nicholas 2025 P6 Prelim P2 Q14",
"image_needed": true,
"image_options": false,
"image_file": "p2q14.png",
"image_page": 38,
"image_bbox": [0.20, 0.10, 0.80, 0.30],
"image_loc": "a 'Greatest Sales Ever!' brochure showing two books, 'Buy first book at 10% discount' and 'Buy second book at [ink-blotted]% discount', upper part of page 38",
"notes": "Key: P2 Q14 (a) $11.25, (b) $12.50, (c) discount of 2nd book = 20% (a fraction-free % — captured in notes). answer0 = 11.25 for (a), answer1 = 12.50 for (b). Part (c) (20%) needs (b) and saved-$3.70 info; recorded here."
},
{
"n": 45,
"type_id": 0,
"question": "In the grid, AB and BC are straight lines.
(a) Measure and write down the size of ∠ABC.
(b) AB and BC are two sides of a trapezium ABCD. BA is parallel to CD. CD is 2 units longer than BA. Complete the drawing of trapezium ABCD.
(c) CD is also one of the sides of an isosceles triangle CDE. CD = DE. Draw triangle CDE.
(d) Draw rectangle DEFG such that it has the same area as triangle CDE. Rectangle DEFG must not overlap with trapezium ABCD and triangle CDE.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 201,
"difficulty_id": 3,
"explanation": "(a) Measuring on the grid, ∠ABC = 135°. (b)-(d) are construction/drawing tasks: complete the trapezium with CD parallel to BA and 2 units longer, draw the isosceles triangle CDE (CD = DE), then draw a rectangle DEFG of equal area to triangle CDE without overlapping. (See the answer key diagram.)",
"hints": ["(a) Use a protractor on the grid: ∠ABC = 135°.", "Build each shape step by step on the grid using the parallel and equal-area conditions."],
"source": "St Nicholas 2025 P6 Prelim P2 Q15",
"image_needed": true,
"image_options": false,
"image_file": "p2q15.png",
"image_page": 40,
"image_bbox": [0.16, 0.16, 0.80, 0.55],
"image_loc": "a dot grid (1 unit marked) with two line segments AB and BC drawn and labelled A, B, C, upper part of page 40",
"notes": "Interactive draw/measure-and-construct task - type_id 0, skipped on insert. Key: (a) ∠ABC = 135°; (b)-(d) construction diagrams shown in the answer key. The (a) value 135° is recorded here."
},
{
"n": 46,
"type_id": 2,
"question": "Paul and Zalim went out together with a total of $140.20. Zalim spent 4 times as much money as Paul. The amount of money Paul had left was $12 more than \\(\\dfrac{1}{2}\\) of what Zalim spent. The amount of money Zalim had left was \\(\\dfrac{1}{5}\\) of what Paul had left.
(a) How much money did Paul spend? $[?]
(b) How much money did Zalim have at first? $[?]",
"answer0": "17",
"answer1": "77.20",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 241,
"difficulty_id": 3,
"explanation": "Let Paul spend = 1 unit, Zalim spend = 4 units. Paul left = 1/2 x (4 units) + $12 = 2 units + $12. Zalim left = 1/5 of Paul left. Total = (Paul spent + Paul left) + (Zalim spent + Zalim left) = $140.20. From the key: 37 units + $12 + $2.40 = $140.20, so 37 units = $125.80, 1 unit = $3.40, Paul spent = 5 units... the key gives Paul spend (5 unit) = $17. (b) Zalim at first = 22 units + $2.40 = 22 x $3.40 + $2.40 = $77.20. Answers: (a) $17, (b) $77.20.",
"hints": ["Set up units for Paul and Zalim's spending and 'left' amounts, then total to $140.20.", "Key: 37 units = $125.80, 1 unit = $3.40; Paul spent = $17, Zalim at first = $77.20."],
"source": "St Nicholas 2025 P6 Prelim P2 Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: P2 Q16 (a) $17, (b) $77.20. answer0 = 17 for (a), answer1 = 77.20 for (b)."
},
{
"n": 47,
"type_id": 2,
"question": "A footpath of length 25.2 m is tiled using identical rectangular tiles and identical circular tiles, following the pattern shown. Each tile is in contact with those next to it. The width of the footpath is 84 cm. (Take π = \\(\\dfrac{22}{7}\\))
(a) How many rectangular and circular tiles were used to tile the entire footpath altogether? [?]
(b) Find the area of the footpath not covered by tiles. [?] cm²
(c) Replacing all tiles costs $3.20 per circular tile and $1.80 per rectangular tile. What is the total cost to replace all the tiles on the footpath? $[?]",
"answer0": "140",
"answer1": "15120",
"answer2": "560",
"answer3": null,
"correct_answer": null,
"skill_id": 222,
"difficulty_id": 3,
"explanation": "(a) 25.2 m = 2520 cm. The repeating block: 84 / 2 = 42 (each small square 42 cm... ), 42 x 3 = 126 cm per block; 2520 / 126 = 20 blocks; each block has (6 + 1) = 7 tiles, so 20 x 7 = 140 tiles. (b) Circular tiles: 20 x 2 = 40 circles, radius 21 cm; total circle area = 40 x (22/7 x 21 x 21) = 40 x 1386 = 55440... ; the key computes per-block 1764 (square area) minus 1386 (circle) then x 40 = 15120 cm². (c) Circular tiles 40 x $3.20 = $128; rectangular tiles 240 x $1.80 = $432; total $128 + $432 = $560. Answers: (a) 140 tiles, (b) 15120 cm², (c) $560.",
"hints": ["(a) Convert 25.2 m = 2520 cm; find the block length and how many blocks fit, then count tiles per block.", "(c) 40 circular tiles x $3.20 + 240 rectangular tiles x $1.80 = $128 + $432 = $560."],
"source": "St Nicholas 2025 P6 Prelim P2 Q17",
"image_needed": true,
"image_options": false,
"image_file": "p2q17.png",
"image_page": 42,
"image_bbox": [0.18, 0.18, 0.70, 0.32],
"image_loc": "a footpath tiling pattern of rectangular tiles arranged around circular tiles, width 84 cm marked with a dashed double-arrow, upper-left of page 42",
"notes": "Key: P2 Q17 (a) 140 tiles, (b) 15120 cm², (c) $560. answer0 = 140 (a), answer1 = 15120 (b), answer2 = 560 (c). Three numeric parts captured as three blanks."
}
]
}