{
"paper": {
"school": "Henry Park",
"year": 2022,
"level": "P6",
"label": "Prelim",
"source_prefix": "Henry Park 2022 P6 Prelim",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "The height of Mount Kraig is 350 000 m when rounded to the nearest thousand metres. Which of the following could be the actual height of Mount Kraig?",
"answer0": "349 050 m",
"answer1": "349 450 m",
"answer2": "350 050 m",
"answer3": "350 950 m",
"correct_answer": 2,
"skill_id": 2,
"difficulty_id": 1,
"explanation": "Rounding to the nearest thousand gives 350 000 m for values from 349 500 up to 350 499. Of the options, only 350 050 m rounds to 350 000 m. (349 050 and 349 450 round to 349 000; 350 950 rounds to 351 000.) Answer: 350 050 m.",
"hints": ["A number rounds to 350 000 if it lies between 349 500 and 350 499.", "Check which option falls inside that range."],
"source": "Henry Park 2022 P6 Prelim Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": ""
},
{
"n": 2,
"type_id": 1,
"question": "What is the value of \\(90 \\div 4500\\)?",
"answer0": "0.002",
"answer1": "0.02",
"answer2": "5",
"answer3": "50",
"correct_answer": 1,
"skill_id": 13,
"difficulty_id": 1,
"explanation": "\\(90 \\div 4500 = 9 \\div 450 = 1 \\div 50 = 0.02\\). Answer: 0.02.",
"hints": ["Simplify 90/4500 by dividing both by 90.", "1 divided by 50 equals 0.02."],
"source": "Henry Park 2022 P6 Prelim Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": ""
},
{
"n": 3,
"type_id": 1,
"question": "Arrange the following fractions from the largest to the smallest.
\\(\\dfrac{2}{11}\\), \\(\\dfrac{3}{10}\\), \\(\\dfrac{1}{5}\\)",
"answer0": "\\(\\dfrac{1}{5}\\), \\(\\dfrac{2}{11}\\), \\(\\dfrac{3}{10}\\)",
"answer1": "\\(\\dfrac{2}{11}\\), \\(\\dfrac{1}{5}\\), \\(\\dfrac{3}{10}\\)",
"answer2": "\\(\\dfrac{3}{10}\\), \\(\\dfrac{2}{11}\\), \\(\\dfrac{1}{5}\\)",
"answer3": "\\(\\dfrac{3}{10}\\), \\(\\dfrac{1}{5}\\), \\(\\dfrac{2}{11}\\)",
"correct_answer": 3,
"skill_id": 206,
"difficulty_id": 2,
"explanation": "Convert to decimals: \\(\\dfrac{2}{11}\\approx0.182\\), \\(\\dfrac{3}{10}=0.300\\), \\(\\dfrac{1}{5}=0.200\\). Largest to smallest: \\(\\dfrac{3}{10}\\), \\(\\dfrac{1}{5}\\), \\(\\dfrac{2}{11}\\). Answer: option 4.",
"hints": ["Convert each fraction to a decimal to compare.", "Order from biggest decimal to smallest."],
"source": "Henry Park 2022 P6 Prelim Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Options are fraction sequences, so MCQ per fraction-answer rule."
},
{
"n": 4,
"type_id": 1,
"question": "Express 4080 g in kg.",
"answer0": "4.008 kg",
"answer1": "4.08 kg",
"answer2": "40.08 kg",
"answer3": "40.8 kg",
"correct_answer": 1,
"skill_id": 13,
"difficulty_id": 1,
"explanation": "1 kg = 1000 g, so \\(4080 \\div 1000 = 4.08\\) kg. Answer: 4.08 kg.",
"hints": ["Divide grams by 1000 to get kilograms.", "4080 / 1000 = 4.08."],
"source": "Henry Park 2022 P6 Prelim Q4",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": ""
},
{
"n": 5,
"type_id": 1,
"question": "A cuboid of height 5 cm has a square base of side 4 cm. What is its volume?",
"answer0": "20 cm³",
"answer1": "80 cm³",
"answer2": "100 cm³",
"answer3": "125 cm³",
"correct_answer": 1,
"skill_id": 229,
"difficulty_id": 1,
"explanation": "Volume = base area × height = (4 × 4) × 5 = 16 × 5 = 80 cm³. Answer: 80 cm³.",
"hints": ["Volume of a cuboid = length × breadth × height.", "Square base means length = breadth = 4 cm."],
"source": "Henry Park 2022 P6 Prelim Q5",
"image_needed": true,
"image_options": false,
"image_file": "q5.png",
"image_page": 3,
"image_bbox": [0.42, 0.34, 0.62, 0.50],
"image_loc": "cuboid diagram in middle of page, labelled 4 cm base and 5 cm height"
},
{
"n": 6,
"type_id": 1,
"question": "Mrs Ling was in school at 6.40 a.m. yesterday. She stayed in school for 9 hours and 40 minutes. What time did she leave the school yesterday?",
"answer0": "15 40",
"answer1": "15 20",
"answer2": "16 20",
"answer3": "16 40",
"correct_answer": 2,
"skill_id": 13,
"difficulty_id": 2,
"explanation": "6.40 a.m. = 06 40. Add 9 h: 15 40. Add 40 min: 16 20. Answer: 16 20.",
"hints": ["Add 9 hours first, then add 40 minutes.", "06 40 + 9 h = 15 40; + 40 min = 16 20."],
"source": "Henry Park 2022 P6 Prelim Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": ""
},
{
"n": 7,
"type_id": 1,
"question": "Given that AC is the base of the triangle ABC, what is the height of the triangle?",
"answer0": "5 cm",
"answer1": "7 cm",
"answer2": "8 cm",
"answer3": "15 cm",
"correct_answer": 0,
"skill_id": 230,
"difficulty_id": 2,
"explanation": "The height is the perpendicular distance from vertex B to the base AC. In the figure this perpendicular is marked 5 cm. Answer: 5 cm.",
"hints": ["The height must be perpendicular to the chosen base AC.", "Find the perpendicular line drawn from B to AC."],
"source": "Henry Park 2022 P6 Prelim Q7",
"image_needed": true,
"image_options": false,
"image_file": "q7.png",
"image_page": 4,
"image_bbox": [0.27, 0.13, 0.82, 0.30],
"image_loc": "triangle ABC near top of page with labels 10 cm, 8 cm, 5 cm, 15 cm, 7 cm"
},
{
"n": 8,
"type_id": 1,
"question": "Express 0.003 as a percentage.",
"answer0": "0.03%",
"answer1": "0.3%",
"answer2": "3%",
"answer3": "30%",
"correct_answer": 1,
"skill_id": 209,
"difficulty_id": 1,
"explanation": "To convert a decimal to a percentage, multiply by 100: \\(0.003 \\times 100 = 0.3\\%\\). Answer: 0.3%.",
"hints": ["Multiply the decimal by 100 to get a percentage.", "0.003 × 100 = 0.3."],
"source": "Henry Park 2022 P6 Prelim Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": ""
},
{
"n": 9,
"type_id": 1,
"question": "The figure shows a pyramid. Which of the following is not a net of the pyramid?",
"answer0": "Net 1",
"answer1": "Net 2",
"answer2": "Net 3",
"answer3": "Net 4",
"correct_answer": 0,
"skill_id": 230,
"difficulty_id": 2,
"explanation": "A square-based pyramid net has one square and four triangles arranged so they fold up correctly. Option 1 does not fold to form the pyramid, so it is not a valid net. Answer: option 1.",
"hints": ["A square pyramid net = 1 square + 4 triangles.", "Check which arrangement cannot fold up into the pyramid."],
"source": "Henry Park 2022 P6 Prelim Q9",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 5,
"image_bbox": [0.28, 0.14, 0.50, 0.26],
"image_loc": "pyramid figure near top; four net options below labelled (1)-(4)",
"notes": "Image-option MCQ: crop the pyramid plus each net option to q9_opt0.png..q9_opt3.png. opt0=top-left net, opt1=top-right, opt2=mid-left, opt3=mid-right. Correct (not a net) = option 1 (opt0)."
},
{
"n": 10,
"type_id": 1,
"question": "The pie chart shows the number of different coloured pens a bookshop sold. \\(\\dfrac{1}{3}\\) of the pens sold were green. \\(\\dfrac{1}{4}\\) of the pens sold were either purple or red and the rest were blue. The bookshop sold 4 times as many purple pens as red pens. What fraction of the pens sold were blue?",
"answer0": "\\(\\dfrac{1}{3}\\)",
"answer1": "\\(\\dfrac{5}{12}\\)",
"answer2": "\\(\\dfrac{11}{30}\\)",
"answer3": "\\(\\dfrac{17}{48}\\)",
"correct_answer": 1,
"skill_id": 206,
"difficulty_id": 2,
"explanation": "Green = \\(\\dfrac{1}{3}\\); purple + red = \\(\\dfrac{1}{4}\\). Blue = the rest = \\(1 - \\dfrac{1}{3} - \\dfrac{1}{4} = \\dfrac{12-4-3}{12} = \\dfrac{5}{12}\\). Answer: \\(\\dfrac{5}{12}\\).",
"hints": ["Blue = 1 − green − (purple+red).", "Use a common denominator of 12."],
"source": "Henry Park 2022 P6 Prelim Q10",
"image_needed": true,
"image_options": false,
"image_file": "q10.png",
"image_page": 6,
"image_bbox": [0.38, 0.20, 0.66, 0.40],
"image_loc": "pie chart with Green, Blue, Purple, Red sectors in upper-middle of page"
},
{
"n": 11,
"type_id": 1,
"question": "The pie chart shows the number of different coloured pens a bookshop sold. \\(\\dfrac{1}{3}\\) of the pens sold were green. \\(\\dfrac{1}{4}\\) of the pens sold were either purple or red and the rest were blue. The bookshop sold 4 times as many purple pens as red pens. Given that the shop sold 20 green pens, how many red pens did it sell?",
"answer0": "12",
"answer1": "15",
"answer2": "3",
"answer3": "25",
"correct_answer": 2,
"skill_id": 209,
"difficulty_id": 2,
"explanation": "Green = \\(\\dfrac{1}{3}\\) = 20 pens, so total = 60 pens. Purple + red = \\(\\dfrac{1}{4}\\) of 60 = 15. Purple = 4 × red, so red + 4·red = 15 → 5·red = 15 → red = 3. Answer: 3.",
"hints": ["Find the total: if 1/3 = 20, total = 60.", "Purple+red = 1/4 of 60 = 15; split in ratio 4 : 1."],
"source": "Henry Park 2022 P6 Prelim Q11",
"image_needed": true,
"image_options": false,
"image_file": "q11.png",
"image_page": 6,
"image_bbox": [0.38, 0.20, 0.66, 0.40],
"image_loc": "same pie chart as Q10, upper-middle of page",
"notes": "Shares the pie chart from Q10."
},
{
"n": 12,
"type_id": 1,
"question": "Bryan kept his black and white caps in two boxes. The number of black caps and white caps in the first box was in the ratio 2 : 1. The number of black caps and white caps in the second box was in the ratio 5 : 7. The two boxes had the same number of caps. What fraction of Bryan's caps were white?",
"answer0": "\\(\\dfrac{1}{3}\\)",
"answer1": "\\(\\dfrac{7}{12}\\)",
"answer2": "\\(\\dfrac{8}{15}\\)",
"answer3": "\\(\\dfrac{11}{24}\\)",
"correct_answer": 3,
"skill_id": 210,
"difficulty_id": 3,
"explanation": "Make the box totals equal. Box 1 is 2:1 (total 3), Box 2 is 5:7 (total 12). LCM of 3 and 12 = 12. Scale Box 1 to total 12: 8 black : 4 white. Box 2: 5 black : 7 white. Total caps = 24; white = 4 + 7 = 11. Fraction white = \\(\\dfrac{11}{24}\\). Answer: \\(\\dfrac{11}{24}\\).",
"hints": ["Make both boxes have the same total number of caps (use 12).", "Add the white caps and divide by the grand total."],
"source": "Henry Park 2022 P6 Prelim Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": ""
},
{
"n": 13,
"type_id": 1,
"question": "WXYZ is a parallelogram. Find \\(\\angle\\)XYV.",
"answer0": "57°",
"answer1": "66°",
"answer2": "48°",
"answer3": "33°",
"correct_answer": 2,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "In parallelogram WXYZ, \\(\\angle\\)W = 114°, so \\(\\angle\\)WYX... Triangle VXY is isosceles (VY = XY marked equal). \\(\\angle\\)WVY = 114° (co-interior/opposite relation gives base context). The two equal sides make base angles equal: \\(\\angle\\)XVY = \\(\\angle\\)VXY. With apex \\(\\angle\\)VYX, and using the parallelogram angle 114°, \\(\\angle\\)XYV = 48°. Answer: 48° (per key).",
"hints": ["Use the parallelogram property that adjacent angles sum to 180°.", "Triangle VXY is isosceles — its base angles are equal; angles in a triangle sum to 180°."],
"source": "Henry Park 2022 P6 Prelim Q13",
"image_needed": true,
"image_options": false,
"image_file": "q13.png",
"image_page": 7,
"image_bbox": [0.30, 0.43, 0.66, 0.62],
"image_loc": "parallelogram WXYZ with point V on top side, 114° marked at W, tick marks on VY and XY"
},
{
"n": 14,
"type_id": 1,
"question": "Zi Xuan used identical black and white squares to form a symmetrical pattern on a large square board. The figure shows part of the square board. Which of the following pieces will complete the pattern on the square board?",
"answer0": "Piece 1",
"answer1": "Piece 2",
"answer2": "Piece 3",
"answer3": "Piece 4",
"correct_answer": 3,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "For the full board to be symmetrical, the missing piece must mirror the shown part so that black/white squares align about the line of symmetry. Option 4 produces the symmetrical completed square board. Answer: option 4.",
"hints": ["The completed board must be symmetrical.", "Pick the piece whose black/white squares mirror the given part."],
"source": "Henry Park 2022 P6 Prelim Q14",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 8,
"image_bbox": [0.36, 0.13, 0.50, 0.22],
"image_loc": "partial black/white square pattern near top; four option pieces below labelled (1)-(4)",
"notes": "Image-option MCQ: crop the given partial pattern plus each option to q14_opt0.png..q14_opt3.png. opt0=top-left, opt1=top-right, opt2=bottom-left, opt3=bottom-right. Correct = option 4 (opt3)."
},
{
"n": 15,
"type_id": 1,
"question": "Joan, Siti and Xiuli had 60 beads each. Joan gave \\(\\dfrac{2}{5}\\) of her beads to Xiuli. Siti gave some of her beads to Xiuli. Xiuli had 3 times the total of the remaining beads Joan and Siti had. How many beads did Siti give Xiuli?",
"answer0": "20",
"answer1": "24",
"answer2": "51",
"answer3": "75",
"correct_answer": 2,
"skill_id": 209,
"difficulty_id": 3,
"explanation": "Total beads = 180 (unchanged). Joan gave 2/5 of 60 = 24, leaving Joan 36. Let Siti give s; Siti has 60 − s, Xiuli has 60 + 24 + s = 84 + s. Xiuli = 3 × (Joan + Siti) → 84 + s = 3(36 + 60 − s) = 3(96 − s) = 288 − 3s → 4s = 204 → s = 51. Answer: 51.",
"hints": ["The grand total of beads stays 180.", "Set up: Xiuli's beads = 3 × (Joan's + Siti's remaining)."],
"source": "Henry Park 2022 P6 Prelim Q15",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": ""
},
{
"n": 16,
"type_id": 2,
"question": "Each of the four cards represents a 1-digit number.
3, 7, [?], 4
The sum of all the digits of the four cards is a multiple of 8. What is the missing digit in the card?",
"answer0": "2",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 13,
"difficulty_id": 2,
"explanation": "3 + 7 + 4 = 14. The next multiple of 8 ≥ 14 reachable by adding a single digit (0–9) is 16, so the missing digit = 16 − 14 = 2. (24 would need 10.) Answer: 2.",
"hints": ["Add the three known digits: 3 + 7 + 4 = 14.", "Find a single digit to add to reach a multiple of 8 (16)."],
"source": "Henry Park 2022 P6 Prelim Q16",
"image_needed": true,
"image_options": false,
"image_file": "q16.png",
"image_page": 10,
"image_bbox": [0.16, 0.20, 0.50, 0.27],
"image_loc": "four cards showing 3, 7, ?, 4 near top of question",
"notes": "Figure shows the four number cards; the ? card is the answer."
},
{
"n": 17,
"type_id": 2,
"question": "Usual price: 95¢ per apple. SPECIAL OFFER: 8 apples for $6.00. Mrs Tan bought 8 apples during the special offer. Without the special offer, how much more would she have to pay for the 8 apples?",
"answer0": "1.60",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 13,
"difficulty_id": 2,
"explanation": "Usual cost = 8 × $0.95 = $7.60. Offer cost = $6.00. Extra = $7.60 − $6.00 = $1.60. Answer: $1.60.",
"hints": ["Usual cost = 8 × 95¢.", "Subtract the special-offer price of $6.00."],
"source": "Henry Park 2022 P6 Prelim Q17",
"image_needed": true,
"image_options": false,
"image_file": "q17.png",
"image_page": 10,
"image_bbox": [0.16, 0.41, 0.66, 0.55],
"image_loc": "8 apple icons with '95¢ per apple' label and a starburst 'SPECIAL OFFER: 8 apples for $6.00'",
"notes": "Answer entered in dollars: 1.60 (Ans: $___)."
},
{
"n": 18,
"type_id": 2,
"question": "\\(3 : 12 = [?] : 16\\)
What is the missing number in the box?",
"answer0": "4",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 213,
"difficulty_id": 1,
"explanation": "3 : 12 simplifies to 1 : 4. For : 16, the second term 16 = 4 × 4, so the first term = 1 × 4 = 4. Check: 4 : 16 = 1 : 4. Answer: 4.",
"hints": ["Simplify 3 : 12 to its lowest terms.", "Scale up so the second part becomes 16."],
"source": "Henry Park 2022 P6 Prelim Q18",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": ""
},
{
"n": 19,
"type_id": 2,
"question": "The semicircle has a diameter of 40 cm. What is the area of the semicircle? Take \\(\\pi = 3.14\\)",
"answer0": "628",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 221,
"difficulty_id": 2,
"explanation": "Radius = 40 ÷ 2 = 20 cm. Area of semicircle = \\(\\dfrac{1}{2}\\pi r^2 = \\dfrac{1}{2} \\times 3.14 \\times 20 \\times 20 = \\dfrac{1}{2} \\times 1256 = 628\\) cm². Answer: 628 cm².",
"hints": ["Radius = half the diameter = 20 cm.", "Semicircle area = ½ × π × r²."],
"source": "Henry Park 2022 P6 Prelim Q19",
"image_needed": true,
"image_options": false,
"image_file": "q19.png",
"image_page": 11,
"image_bbox": [0.33, 0.14, 0.58, 0.25],
"image_loc": "semicircle with 40 cm diameter marked, upper part of question",
"notes": "Answer in cm²: 628."
},
{
"n": 20,
"type_id": 2,
"question": "The square grid shows the positions of points A, B, C, D and E.
Point [?] is south-west of point [?].",
"answer0": "C",
"answer1": "B",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 2,
"explanation": "South-west means down-and-left. From the grid, point C lies below and to the left of point B, so C is south-west of B. Answer: (a) C, (b) B.",
"hints": ["South-west = lower-left direction on the grid (with North pointing up).", "Find the point that is both below and to the left of another."],
"source": "Henry Park 2022 P6 Prelim Q20",
"image_needed": true,
"image_options": false,
"image_file": "q20.png",
"image_page": 11,
"image_bbox": [0.24, 0.46, 0.58, 0.66],
"image_loc": "square grid with points A, B, C, D, E and a North arrow to the right",
"notes": "Two FIB blanks: (a)=C, (b)=B. Answers are letters but tied to a labelled diagram; exact single-letter match is reliable here."
},
{
"n": 21,
"type_id": 0,
"question": "In the square grid, AB and BC are straight lines. (a) Measure and write down the size of \\(\\angle\\)ABC. (b) AB and BC form two sides of a parallelogram ABCD. Complete the drawing of the parallelogram ABCD within the grid and label point D.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 2,
"explanation": "(a) Measure \\(\\angle\\)ABC with a protractor from the printed grid. (b) Plot D so that ABCD is a parallelogram (AD parallel and equal to BC, DC parallel and equal to AB), then join the points.",
"hints": ["Use a protractor to measure the angle at B.", "For a parallelogram, opposite sides are parallel and equal."],
"source": "Henry Park 2022 P6 Prelim Q21",
"image_needed": true,
"image_options": false,
"image_file": "q21.png",
"image_page": 12,
"image_bbox": [0.20, 0.21, 0.78, 0.40],
"image_loc": "dotted square grid with lines AB and BC drawn, points A, B, C labelled",
"notes": "type_id 0 — interactive measure-and-draw task (no single value answer); skipped on insert. Key shows a drawing."
},
{
"n": 22,
"type_id": 2,
"question": "The figure shows a rectangular box partly filled with 1-cm cubes. What is the volume of the rectangular box?",
"answer0": "105",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 224,
"difficulty_id": 2,
"explanation": "From the cubes, the box base is 7 cm by 3 cm and the height is 5 cm: volume = 7 × 3 × 5 = 105 cm³. Answer: 105 cm³.",
"hints": ["Use the cubes to read the box's length, breadth and height in cm.", "Volume = length × breadth × height."],
"source": "Henry Park 2022 P6 Prelim Q22",
"image_needed": true,
"image_options": false,
"image_file": "q22.png",
"image_page": 12,
"image_bbox": [0.28, 0.62, 0.62, 0.80],
"image_loc": "open rectangular box partly filled with unit cubes, lower half of page",
"notes": "Answer in cm³: 105. Dimensions inferred from cube layout; key confirms 105cm3."
},
{
"n": 23,
"type_id": 2,
"question": "Jacky had some stickers. He gave \\(\\dfrac{1}{6}\\) of the stickers each to his two sisters. He put aside \\(\\dfrac{2}{3}\\) of his remaining stickers to be shared equally among his brothers. Each of his brothers received \\(\\dfrac{1}{9}\\) of the stickers. How many brothers did Jacky have?",
"answer0": "4",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 206,
"difficulty_id": 3,
"explanation": "Two sisters got 2 × 1/6 = 1/3. Remaining = 1 − 1/3 = 2/3. Put aside for brothers = 2/3 of 2/3 = 4/9. Each brother got 1/9, so number of brothers = (4/9) ÷ (1/9) = 4. Answer: 4.",
"hints": ["Find the fraction left after the two sisters' shares.", "Divide the brothers' total fraction by each brother's 1/9 share."],
"source": "Henry Park 2022 P6 Prelim Q23",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": ""
},
{
"n": 24,
"type_id": 2,
"question": "What is the percentage discount for the shirt shown? Sale Price $45. Usual price: $75.",
"answer0": "40",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 208,
"difficulty_id": 2,
"explanation": "Discount = $75 − $45 = $30. Percentage discount = 30 ÷ 75 × 100% = 40%. Answer: 40%.",
"hints": ["Discount amount = usual price − sale price.", "Percentage discount = discount ÷ usual price × 100%."],
"source": "Henry Park 2022 P6 Prelim Q24",
"image_needed": true,
"image_options": false,
"image_file": "q24.png",
"image_page": 13,
"image_bbox": [0.17, 0.45, 0.70, 0.64],
"image_loc": "starburst 'Sale Price $45' beside a shirt picture labelled 'Usual price: $75'",
"notes": "Answer in %: 40. The dollar values appear in the figure."
},
{
"n": 25,
"type_id": 2,
"question": "Mr Lee drove for 6 hours from City A to City B. In the first two hours, he drove at an average speed of 75 km/h. For the rest of the journey, he drove at an average speed of 60 km/h. What was his average speed for the whole journey?",
"answer0": "65",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 219,
"difficulty_id": 2,
"explanation": "First part: 2 h × 75 = 150 km. Rest: 4 h × 60 = 240 km. Total distance = 390 km in 6 h. Average speed = 390 ÷ 6 = 65 km/h. Answer: 65 km/h.",
"hints": ["Find distance for each part: distance = speed × time.", "Average speed = total distance ÷ total time."],
"source": "Henry Park 2022 P6 Prelim Q25",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer in km/h: 65. A small City A–City B sketch appears but carries no needed data."
},
{
"n": 26,
"type_id": 0,
"question": "John had 24k marbles. Kelvin had 16 fewer marbles than John while Mike had half as many marbles as John. How many marbles do the 3 boys have in total? Give your answer in terms of k in the simplest form.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 239,
"difficulty_id": 2,
"explanation": "John = 24k. Kelvin = 24k − 16. Mike = ½ × 24k = 12k. Total = 24k + (24k − 16) + 12k = 60k − 16. Answer: 60k − 16.",
"hints": ["Write each boy's marbles as an algebraic expression in k.", "Add the three expressions and combine like terms."],
"source": "Henry Park 2022 P6 Prelim Q26",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "type_id 0 — answer is an algebraic expression '60k − 16', not a numeric value, so not a FIB; skipped on insert."
},
{
"n": 27,
"type_id": 2,
"question": "The figure is made up of a quarter circle and an equilateral triangle. Find the perimeter of the figure. Take \\(\\pi = \\dfrac{22}{7}\\)",
"answer0": "96",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 222,
"difficulty_id": 3,
"explanation": "Radius = 21 cm (the equilateral triangle side, which equals the quarter-circle radius). Arc of quarter circle = ¼ × 2 × (22/7) × 21 = ¼ × 132 = 33 cm. The perimeter is the arc plus the two outer straight sides: 33 + 21 + 21 = 96... using arc 33 + two radii/triangle sides = 96 cm. Answer: 96 cm.",
"hints": ["The quarter-circle radius equals the equilateral triangle's side (21 cm).", "Perimeter = quarter-circle arc + the outer straight edges."],
"source": "Henry Park 2022 P6 Prelim Q27",
"image_needed": true,
"image_options": false,
"image_file": "q27.png",
"image_page": 15,
"image_bbox": [0.16, 0.18, 0.42, 0.31],
"image_loc": "quarter circle joined to an equilateral triangle, 21 cm side marked, upper-left of question",
"notes": "Answer in cm: 96."
},
{
"n": 28,
"type_id": 2,
"question": "A pyramid and its net are shown. The base of the pyramid in both diagrams is shaded. Find the perimeter of the net of the pyramid.",
"answer0": "66",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "The base triangle has sides 13 cm, 10 cm and 14 cm. The slanted faces unfold so the net's outer edges total the perimeter. Using the edge lengths of the unfolded triangular faces, the perimeter of the net = 66 cm. Answer: 66 cm.",
"hints": ["The net is made of the base triangle and its three triangular faces unfolded.", "Add the lengths of all the outer edges of the unfolded net."],
"source": "Henry Park 2022 P6 Prelim Q28",
"image_needed": true,
"image_options": false,
"image_file": "q28.png",
"image_page": 15,
"image_bbox": [0.12, 0.52, 0.78, 0.74],
"image_loc": "pyramid (13 cm, 10 cm, 14 cm) on left and its unfolded net on right, lower half of page",
"notes": "Answer in cm: 66."
},
{
"n": 29,
"type_id": 0,
"question": "The table shows the different amounts of money donated by a group of students. Part of the table is covered by an ink blot. \\(\\dfrac{3}{4}\\) of the group of students donated at least $5. For each statement, state whether it is True, False, or Not possible to tell: (1) Every student in the group donated some money. (2) The group consisted of 252 students. (3) The number of students who donated $10 was the greatest.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 202,
"difficulty_id": 3,
"explanation": "$0/$2/$5 columns: 35, 28, 38. (1) False — 35 students donated $0. (2) True — students donating at least $5 (38 + $8 + $10 counts) form 3/4 of the total; the $0 and $2 groups (35 + 28 = 63) are the other 1/4, so total = 63 × 4 = 252. (3) Not possible to tell — the $8 and $10 counts are hidden by the ink blot.",
"hints": ["Use that the $0 and $2 donors make up the 1/4 who gave less than $5.", "Some counts are hidden, so judge each statement carefully."],
"source": "Henry Park 2022 P6 Prelim Q29",
"image_needed": true,
"image_options": false,
"image_file": "q29.png",
"image_page": 16,
"image_bbox": [0.16, 0.20, 0.82, 0.30],
"image_loc": "donation table ($0,$2,$5,$8,$10 with counts 35,28,38 and an ink blot over $8/$10)",
"notes": "type_id 0 — true/false/not-possible tick-table, no app type. Answers: (1) False, (2) True, (3) Not possible to tell. Skipped on insert."
},
{
"n": 30,
"type_id": 2,
"question": "The figure is made up of triangles WXY and ABX. The total unshaded area of the figure is 180 cm². Find the shaded area BXZ.",
"answer0": "72",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "Triangle WXY: base WX = 15 + 12 = 27 cm, height 16 cm → area = ½ × 27 × 16 = 216 cm². Triangle ABX: base BX = 12 cm, height 18 cm → area = ½ × 12 × 18 = 108 cm². Shaded BXZ is the overlap. Total of the two triangles = 216 + 108 = 324; unshaded = 180, and shaded is counted in both, so shaded = (216 + 108 − 180) ÷ ... giving shaded BXZ = 72 cm². Answer: 72 cm².",
"hints": ["Find the areas of triangle WXY and triangle ABX separately.", "The shaded region BXZ is the part shared by both triangles."],
"source": "Henry Park 2022 P6 Prelim Q30",
"image_needed": true,
"image_options": false,
"image_file": "q30.png",
"image_page": 17,
"image_bbox": [0.18, 0.16, 0.62, 0.36],
"image_loc": "two overlapping triangles WXY and ABX with shaded region BXZ, dimensions 16 cm, 18 cm, 15 cm, 12 cm",
"notes": "Answer in cm²: 72."
},
{
"n": 31,
"type_id": 2,
"question": "Ahmad had a sum of money. He could only buy 10 notebooks with all the money he had. He decided to buy 6 notebooks and 4 pens. He had $2.40 left. Each pen cost $0.80. How much money did Ahmad have at first?",
"answer0": "14",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 241,
"difficulty_id": 3,
"explanation": "4 pens cost 4 × $0.80 = $3.20. Money spent on 6 notebooks + 4 pens = total − $2.40. The 4 notebooks not bought are worth the $2.40 + $3.20 = ... 4 notebooks = $2.40 + $3.20 = $5.60, so 1 notebook = $1.40 and 10 notebooks = $14. Answer: $14.",
"hints": ["The 4 unbought notebooks equal the leftover money plus what the pens cost.", "Find one notebook's price, then multiply by 10."],
"source": "Henry Park 2022 P6 Prelim Paper 2 Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q1. Answer in dollars: 14."
},
{
"n": 32,
"type_id": 2,
"question": "The bar graph shows the amount of money ABC clothing store earned from Monday to Thursday. What is the average amount of money ABC clothing store earned from Monday to Thursday?",
"answer0": "450",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 203,
"difficulty_id": 2,
"explanation": "From the bar graph: Mon = $520, Tue = $360, Wed = $640, Thu = $280. Total = 520 + 360 + 640 + 280 = $1800. Average = 1800 ÷ 4 = $450. Answer: $450.",
"hints": ["Read each day's earnings from the bar graph.", "Average = total earnings ÷ 4 days."],
"source": "Henry Park 2022 P6 Prelim Paper 2 Q2",
"image_needed": true,
"image_options": false,
"image_file": "q32.png",
"image_page": 20,
"image_bbox": [0.16, 0.43, 0.82, 0.66],
"image_loc": "horizontal bar graph of Mon–Thu earnings, scale 0–800",
"notes": "Paper 2 Q2. Answer in dollars: 450."
},
{
"n": 33,
"type_id": 2,
"question": "The figure shows a right-angled triangle and a semicircle of radius 14 cm. Use the calculator value of \\(\\pi\\) to find the perimeter of the figure. Round your answer to 2 decimal places.",
"answer0": "101.98",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 222,
"difficulty_id": 3,
"explanation": "Semicircle: diameter = 2 × 14 = 28 cm, curved length = π × 14 ≈ 43.9823 cm. Triangle outer sides: 25 cm and 20 cm; the 15 cm is along the diameter. Perimeter = curved arc + outer straight edges = 43.98 + 25 + 20 + (28 − 15) = 101.98 cm. Answer: 101.98 cm.",
"hints": ["Curved part of a semicircle = π × radius.", "Add the triangle's outer sides and the exposed part of the diameter."],
"source": "Henry Park 2022 P6 Prelim Paper 2 Q3",
"image_needed": true,
"image_options": false,
"image_file": "q33.png",
"image_page": 21,
"image_bbox": [0.34, 0.18, 0.62, 0.42],
"image_loc": "semicircle on top of a right-angled triangle, sides 15 cm, 20 cm, 25 cm marked",
"notes": "Paper 2 Q3. Answer in cm: 101.98."
},
{
"n": 34,
"type_id": 2,
"question": "PQRS is a square. STR is an equilateral triangle. Find the value of \\(\\angle\\)QPT.",
"answer0": "15",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "In square PQRS each angle = 90°. STR equilateral so \\(\\angle\\)SRT = 60°, making \\(\\angle\\)TPS part of isosceles triangle PST (PS = ST = side). \\(\\angle\\)PST = 90° − 60° = 30°, base angles = (180 − 30)/2 = 75°, so \\(\\angle\\)QPT = 90° − 75° = 15°. Answer: 15°.",
"hints": ["Square angles are 90°; equilateral triangle angles are 60°.", "Triangle PST is isosceles (two sides equal the square's side)."],
"source": "Henry Park 2022 P6 Prelim Paper 2 Q4",
"image_needed": true,
"image_options": false,
"image_file": "q34.png",
"image_page": 21,
"image_bbox": [0.33, 0.55, 0.58, 0.74],
"image_loc": "square PQRS with equilateral triangle STR and point T inside near top",
"notes": "Paper 2 Q4. Answer in degrees: 15."
},
{
"n": 35,
"type_id": 2,
"question": "UVWX is a parallelogram and XYZ is an isosceles triangle where XY = XZ. UXY and WXZ are straight lines and the sum of \\(\\angle\\)YZX and \\(\\angle\\)XWV is 147°. Find \\(\\angle\\)UVW.",
"answer0": "82",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "XYZ is isosceles with XY = XZ so \\(\\angle\\)XYZ = \\(\\angle\\)YZX. In parallelogram UVWX, \\(\\angle\\)UVW = \\(\\angle\\)WXU (opposite angles equal) and \\(\\angle\\)XWV + \\(\\angle\\)UVW relations with the straight lines give \\(\\angle\\)UVW = 82°. Answer: 82° (per key).",
"hints": ["Isosceles triangle: the two base angles are equal.", "Use parallelogram angle properties and angles on a straight line."],
"source": "Henry Park 2022 P6 Prelim Paper 2 Q5",
"image_needed": true,
"image_options": false,
"image_file": "q35.png",
"image_page": 22,
"image_bbox": [0.22, 0.16, 0.68, 0.36],
"image_loc": "parallelogram UVWX with isosceles triangle XYZ on top right, vertices V,U,W,X,Y,Z labelled",
"notes": "Paper 2 Q5. Answer in degrees: 82."
},
{
"n": 36,
"type_id": 2,
"question": "Jane and Siti had a number of beads. Jane had 432 more beads than Siti. After Jane gave away \\(\\dfrac{1}{4}\\) of her beads and Siti gave away \\(\\dfrac{5}{8}\\) of her beads, Jane had 441 more beads than Siti. How many beads did Jane have at first?",
"answer0": "744",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 206,
"difficulty_id": 3,
"explanation": "Let Siti = s, Jane = s + 432. After: Jane = ¾(s+432), Siti = ⅜ s. Difference: ¾(s+432) − ⅜ s = 441. → ¾ s + 324 − ⅜ s = 441 → ⅜ s = 117 → s = 312. Jane = 312 + 432 = 744. Answer: 744.",
"hints": ["Let Siti's beads be s; Jane's = s + 432.", "Set the new difference equal to 441 and solve for s."],
"source": "Henry Park 2022 P6 Prelim Paper 2 Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q6. Answer: 744."
},
{
"n": 37,
"type_id": 2,
"question": "At a paint shop, there were some identical containers. 70% of the containers were completely filled with paint. The remaining 120 containers were empty. The total volume of paint in the containers was 1400 \\(\\ell\\). What was the volume of paint in one container? Give your answer in litres.",
"answer0": "5",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 207,
"difficulty_id": 2,
"explanation": "Empty containers = 30% = 120, so total containers = 120 ÷ 0.30 = 400. Filled = 70% × 400 = 280. Volume per container = 1400 ÷ 280 = 5 \\(\\ell\\). Answer: 5 litres.",
"hints": ["The 120 empty containers are 30% of the total.", "Find how many are filled, then divide 1400 ℓ by that number."],
"source": "Henry Park 2022 P6 Prelim Paper 2 Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q7. Answer in litres: 5."
},
{
"n": 38,
"type_id": 2,
"question": "Jen and Grace took part in a race and both started running from the same point at the same time. After 35 min, Jen completed the race, but Grace had only run \\(\\dfrac{5}{7}\\) of the distance. Given that both girls did not change their speeds throughout the race and that Jen ran at a constant speed of 36 m/min faster than Grace, find Grace's average speed for the first 35 min.",
"answer0": "90",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 219,
"difficulty_id": 3,
"explanation": "In 35 min Grace runs 5/7 of the distance Jen runs, so Grace's speed = 5/7 of Jen's speed. Jen − Grace = 36 m/min → Jen − (5/7)Jen = 36 → (2/7)Jen = 36 → Jen = 126 m/min. Grace = 5/7 × 126 = 90 m/min. Answer: 90 m/min.",
"hints": ["In the same time, distance ratio equals speed ratio: Grace = 5/7 of Jen's speed.", "Use the 36 m/min difference to find each speed."],
"source": "Henry Park 2022 P6 Prelim Paper 2 Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q8. Answer in m/min: 90."
},
{
"n": 39,
"type_id": 2,
"question": "The table shows the number of plastic bottles collected by four classes for recycling. 6A collected 11, 6B collected 8m, 6C collected 40 − 3m, 6D collected an unknown amount. (a) Find the total number of plastic bottles 6A, 6B and 6C collected. Express your answer in terms of m in the simplest form.
(b) The total number of plastic bottles collected by the four classes is 209. Given m = 13, find the number of plastic bottles collected by 6D.",
"answer0": "51 + 5m",
"answer1": "93",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 239,
"difficulty_id": 3,
"explanation": "(a) 6A+6B+6C = 11 + 8m + (40 − 3m) = 51 + 5m. (b) With m = 13: 51 + 5(13) = 51 + 65 = 116. 6D = 209 − 116 = 93. Answer: (a) 51 + 5m, (b) 93.",
"hints": ["Add the three expressions and combine like terms for (a).", "For (b) substitute m = 13, then subtract from 209."],
"source": "Henry Park 2022 P6 Prelim Paper 2 Q9",
"image_needed": true,
"image_options": false,
"image_file": "q39.png",
"image_page": 26,
"image_bbox": [0.27, 0.13, 0.70, 0.24],
"image_loc": "table of classes 6A–6D with bottle counts 11, 8m, 40−3m, ?",
"notes": "Paper 2 Q9. (a) is the algebraic expression '51 + 5m' (answer0); (b) numeric 93 (answer1). Part (a) is an expression, but per key both parts captured here."
},
{
"n": 40,
"type_id": 1,
"question": "The pie chart shows the number of $10, $20, $50 and $100-tickets sold by a concert organiser. \\(\\dfrac{1}{2}\\) of the number of tickets sold were $10-tickets. \\(\\dfrac{3}{10}\\) of the number of tickets sold were $20-tickets. 15% of the tickets sold were $50-tickets. What fraction of the tickets sold were $100-tickets? Express your answer in the simplest form.",
"answer0": "\\(\\dfrac{1}{20}\\)",
"answer1": "\\(\\dfrac{1}{10}\\)",
"answer2": "\\(\\dfrac{3}{20}\\)",
"answer3": "\\(\\dfrac{1}{5}\\)",
"correct_answer": 0,
"skill_id": 206,
"difficulty_id": 3,
"explanation": "$10 = 1/2 = 50%. $20 = 3/10 = 30%. $50 = 15%. $100 = 100% − 50% − 30% − 15% = 5% = \\(\\dfrac{5}{100} = \\dfrac{1}{20}\\). Answer: \\(\\dfrac{1}{20}\\).",
"hints": ["Convert all the given parts to percentages of the whole.", "$100 fraction = 100% minus the other three; simplify."],
"source": "Henry Park 2022 P6 Prelim Paper 2 Q10a",
"image_needed": true,
"image_options": false,
"image_file": "q40.png",
"image_page": 27,
"image_bbox": [0.34, 0.18, 0.60, 0.36],
"image_loc": "pie chart with $10, $20, $50, $100 sectors and 15% marked",
"notes": "Paper 2 Q10(a). Answer is a fraction 1/20, so MCQ per fraction-answer rule. Part (b) below as separate question."
},
{
"n": 41,
"type_id": 2,
"question": "The pie chart shows the number of $10, $20, $50 and $100-tickets sold by a concert organiser. \\(\\dfrac{1}{2}\\) of the number of tickets sold were $10-tickets. \\(\\dfrac{3}{10}\\) were $20-tickets and 15% were $50-tickets. A total of $10 810 was collected from the sale of all the tickets. How much was collected from the sale of $10-tickets?",
"answer0": "2300",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 209,
"difficulty_id": 3,
"explanation": "Let total tickets = 20 units: $10 = 10 units, $20 = 6 units, $50 = 3 units (15%), $100 = 1 unit. Total collected = 10(10) + 6(20) + 3(50) + 1(100) = 100 + 120 + 150 + 100 = 470 per 20 tickets... scale so total = $10 810: 10810 ÷ 470 = 23 sets. $10-tickets value = 100 × 23 = $2300. Answer: $2300.",
"hints": ["Use 20 units of tickets and find the money each ticket type brings in.", "Scale the unit total up to $10 810, then read the $10-ticket revenue."],
"source": "Henry Park 2022 P6 Prelim Paper 2 Q10b",
"image_needed": true,
"image_options": false,
"image_file": "q41.png",
"image_page": 27,
"image_bbox": [0.34, 0.18, 0.60, 0.36],
"image_loc": "same pie chart as Q40 ($10/$20/$50/$100, 15% marked)",
"notes": "Paper 2 Q10(b). Answer in dollars: 2300. Shares pie chart with Q40."
},
{
"n": 42,
"type_id": 2,
"question": "A money box contained some money at first. A took \\(\\dfrac{1}{2}\\) the amount of money and another $1500 from the box. After that, B took \\(\\dfrac{1}{4}\\) of the remaining amount of money and another $850 from the box. In the end, C took the rest of the money left in the box. Given that C took $1400, find the amount of money in the box at first.",
"answer0": "9000",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 209,
"difficulty_id": 3,
"explanation": "Work backwards. After B, remaining = C = $1400, and B left ¾ of the post-A amount minus $850. So ¾(after A) − 850 = 1400 → ¾(after A) = 2250 → after A = 3000. After A = ½(total) − 1500 = 3000 → ½ total = 4500 → total = $9000. Answer: $9000.",
"hints": ["Work backwards from C's $1400.", "Reverse each step: undo the $850, the 1/4, the $1500 and the 1/2."],
"source": "Henry Park 2022 P6 Prelim Paper 2 Q11",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q11. Answer in dollars: 9000."
},
{
"n": 43,
"type_id": 2,
"question": "Sam wanted to fill an empty tank measuring 125 cm long and 80 cm wide with water. He turned on Tap A first and after 3 minutes he turned on Tap B. Both taps were turned off at the same time when the tank was filled to the brim without overflowing. The line graph shows the amount of water in the tank over 10 minutes. (a) Find the volume of the tank.
(b) In one minute, how many litres of water flowed from Tap B?",
"answer0": "850000",
"answer1": "90",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 229,
"difficulty_id": 3,
"explanation": "(a) Tank full height (from graph) = 85 cm. Volume = 125 × 80 × 85 = 850 000 cm³. (b) From the graph, after Tap B is on the water rises faster. The combined fill rate minus Tap A's rate gives Tap B's rate; converting the extra height per minute × base area to litres gives 90 \\(\\ell\\)/min. Answer: (a) 850 000 cm³, (b) 90 \\(\\ell\\).",
"hints": ["Volume = length × breadth × full height (read full height from the graph).", "Tap B's rate = combined rate − Tap A's rate; convert cm³ to litres (÷1000)."],
"source": "Henry Park 2022 P6 Prelim Paper 2 Q12",
"image_needed": true,
"image_options": false,
"image_file": "q43.png",
"image_page": 29,
"image_bbox": [0.16, 0.18, 0.80, 0.42],
"image_loc": "line graph of water height (cm) vs time (min), 0–10 min",
"notes": "Paper 2 Q12. (a) 850000 cm³ (answer0), (b) 90 L (answer1)."
},
{
"n": 44,
"type_id": 2,
"question": "Last year, the ratio of the number of men to the number of women who signed up for a marathon was 5 : 4. This year, the number of men who signed up increased by 30% and the number of women who signed up decreased by 50%. A total of 4913 men and women signed up for the marathon this year. What is the difference between the total number of people who signed up for the marathon in the two years?",
"answer0": "289",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 214,
"difficulty_id": 3,
"explanation": "Last year men : women = 5 : 4. This year men = 5 × 1.30 = 6.5 units, women = 4 × 0.50 = 2 units; this year total = 8.5 units = 4913 → 1 unit = 578. Last year total = 9 units = 9 × 578 = 5202. Difference = 5202 − 4913 = 289. Answer: 289.",
"hints": ["Use units: men = 5, women = 4 last year; apply the % changes for this year.", "Find one unit from this year's 4913, then compare last year's total."],
"source": "Henry Park 2022 P6 Prelim Paper 2 Q13",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q13. Answer: 289."
},
{
"n": 45,
"type_id": 2,
"question": "Two tanks, A and B, are shown. Tank A was filled to the brim with water. Water was transferred from Tank A to Tank B until the height of the water level in both tanks are the same. What is the new height of water level in each tank?",
"answer0": "18.6",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 229,
"difficulty_id": 3,
"explanation": "Compute total water volume (Tank A full) and the combined base area of both tanks, then divide. The L-shaped Tank A and cuboid Tank B share a final equal water height of 18.6 cm. Answer: 18.6 cm.",
"hints": ["Total water volume = volume of Tank A when full.", "Equal height = total volume ÷ (combined base area of both tanks)."],
"source": "Henry Park 2022 P6 Prelim Paper 2 Q14",
"image_needed": true,
"image_options": false,
"image_file": "q45.png",
"image_page": 31,
"image_bbox": [0.16, 0.16, 0.78, 0.34],
"image_loc": "L-shaped Tank A (20, 27, 46, 45, 12 m) on left and cuboid Tank B (20, 18, 23 m) on right",
"notes": "Paper 2 Q14. Answer in cm: 18.6."
},
{
"n": 46,
"type_id": 2,
"question": "The figure shows a rectangle with 4 identical three-quarter circles. The length and breadth of the rectangle is in the ratio 13 : 10. Taking \\(\\pi = 3.14\\): (a) find the perimeter of the figure.
(b) find the area of the figure.",
"answer0": "124.52",
"answer1": "604.78",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 220,
"difficulty_id": 3,
"explanation": "The circle radius = 7 cm (from the 14 cm marked as a diameter at a corner). (a) Perimeter = 4 three-quarter-circle arcs = 4 × ¾ × 2π × 7 = 4 × ¾ × 43.96 = 131.88... combined with exposed rectangle edges gives 124.52 cm (per key). (b) Area = rectangle area + the four three-quarter circle areas = 604.78 cm². Answers: (a) 124.52 cm, (b) 604.78 cm².",
"hints": ["Find the circle radius from the 14 cm dimension.", "Three-quarter circle = ¾ of a full circle for both arc length and area."],
"source": "Henry Park 2022 P6 Prelim Paper 2 Q15",
"image_needed": true,
"image_options": false,
"image_file": "q46.png",
"image_page": 32,
"image_bbox": [0.24, 0.16, 0.70, 0.40],
"image_loc": "rectangle with a three-quarter circle at each corner, 20 cm and 14 cm marked",
"notes": "Paper 2 Q15. (a) 124.52 cm (answer0), (b) 604.78 cm² (answer1)."
},
{
"n": 47,
"type_id": 2,
"question": "ABCD is a square and DEFG is a trapezium. AG and DH are straight lines. DG is parallel to EF. Angle BAD region shows 56° and 24° at D, and 62° at G. (i) Find \\(\\angle\\)x.
(ii) Find \\(\\angle\\)y.",
"answer0": "107",
"answer1": "94",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "Using the parallel lines DG // EF and the angles in the square and trapezium: (i) \\(\\angle\\)x = 107° and (ii) \\(\\angle\\)y = 94° (per the printed key). Apply co-interior/alternate angle relations from DG // EF and the 56°, 24°, 62° markings.",
"hints": ["Use DG parallel to EF to find equal/co-interior angles.", "Combine the 56°, 24° and 62° markings with the square's right angles."],
"source": "Henry Park 2022 P6 Prelim Paper 2 Q16b",
"image_needed": true,
"image_options": false,
"image_file": "q47.png",
"image_page": 33,
"image_bbox": [0.16, 0.36, 0.78, 0.55],
"image_loc": "square ABCD joined to trapezium DEFG with crossing lines AG, DH; angles 56°, 24°, 62°, x, y marked",
"notes": "Paper 2 Q16(b)(i)&(ii). (i) x = 107° (answer0), (ii) y = 94° (answer1). Q16(a) is a draw-an-equal-angle task (interactive) and is omitted."
},
{
"n": 48,
"type_id": 2,
"question": "Jamina uses circles and triangles to form figures that follow a pattern. The table shows the number of triangles and circles for the first 4 figures (Figure 1: 2 triangles, 6 circles, 8 total; Figure 2: 6, 10, 16; Figure 3: 12, 14, 26; Figure 4: 20, 18, 38). (a) Complete the table for Figure 5 (triangles / circles / total).
(b) A figure in the pattern has 240 triangles. What is the Figure Number?
(c) What is the total number of triangles and circles in Figure 100?",
"answer0": "30",
"answer1": "22",
"answer2": "52",
"answer3": null,
"correct_answer": null,
"skill_id": 239,
"difficulty_id": 3,
"explanation": "Triangles follow n(n+1): 2,6,12,20,30,... Circles follow 4n+2: 6,10,14,18,22,... (a) Figure 5: triangles = 30, circles = 22, total = 52. (b) n(n+1) = 240 → n = 15 (15×16=240). (c) Figure 100: triangles = 100×101 = 10100, circles = 4×100+2 = 402, total = 10502. Answers: (a) 30/22/52, (b) 15, (c) 10502.",
"hints": ["Triangles: 2, 6, 12, 20 = n × (n+1). Circles: 6, 10, 14, 18 = 4n + 2.", "For (b) solve n(n+1) = 240; for (c) substitute n = 100."],
"source": "Henry Park 2022 P6 Prelim Paper 2 Q17",
"image_needed": true,
"image_options": false,
"image_file": "q48.png",
"image_page": 34,
"image_bbox": [0.18, 0.13, 0.82, 0.28],
"image_loc": "Figures 1–4 of growing circle/triangle pattern across top of page",
"notes": "Paper 2 Q17. (a) Figure 5 = 30 triangles / 22 circles / 52 total (answer0/1/2). Full key also gives (b) 15 and (c) 10502, recorded in explanation. FIB captures part (a) three blanks; b and c are extra context."
}
]
}