{
"paper": {
"school": "Nan Hua Primary School",
"year": 2025,
"level": "P6",
"label": "Prelim",
"source_prefix": "Nan Hua 2025 P6 Prelim",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "Eight hundred thousand and fourteen in numerals is ____________.",
"answer0": "80 014",
"answer1": "80 040",
"answer2": "800 014",
"answer3": "800 040",
"correct_answer": 2,
"skill_id": 100,
"difficulty_id": 1,
"explanation": "Eight hundred thousand = 800 000. And fourteen = 14. 800 000 + 14 = 800 014.",
"hints": ["Split into 'eight hundred thousand' and 'fourteen'.", "800 000 + 14 = 800 014."],
"source": "Nan Hua 2025 P6 Prelim Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"image_page": null,
"image_bbox": null,
"image_loc": null,
"notes": "Key: option 3 -> index 2."
},
{
"n": 2,
"type_id": 1,
"question": "In the number line, what is the value represented by A?",
"answer0": "1.125",
"answer1": "1.250",
"answer2": "1.600",
"answer3": "1.750",
"correct_answer": 3,
"skill_id": 101,
"difficulty_id": 2,
"explanation": "The interval from 1 to 2 is divided into 8 equal parts, each of value 0.125. A is at the 6th mark from 1: 1 + 6 x 0.125 = 1.750.",
"hints": ["Count the equal divisions between 1 and 2.", "Each small division is 1/8 = 0.125."],
"source": "Nan Hua 2025 P6 Prelim Q2",
"image_needed": true,
"image_options": false,
"image_file": "q2.png",
"image_page": 2,
"image_bbox": [0.46, 0.41, 0.82, 0.49],
"image_loc": "right of the options, a horizontal number line from 1 to 2 with arrow A",
"notes": "Key: option 4 -> index 3."
},
{
"n": 3,
"type_id": 1,
"question": "12 + 6 ÷ 2 × 3 = ____________.",
"answer0": "13",
"answer1": "21",
"answer2": "27",
"answer3": "45",
"correct_answer": 1,
"skill_id": 102,
"difficulty_id": 1,
"explanation": "Order of operations: 6 ÷ 2 = 3, then 3 × 3 = 9, then 12 + 9 = 21.",
"hints": ["Do division and multiplication before addition, left to right.", "6 ÷ 2 × 3 = 9; 12 + 9 = 21."],
"source": "Nan Hua 2025 P6 Prelim Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"image_page": null,
"image_bbox": null,
"image_loc": null,
"notes": "Key: option 2 -> index 1."
},
{
"n": 4,
"type_id": 1,
"question": "Which pair of lines in the square grid is parallel?",
"answer0": "AF and FE",
"answer1": "AB and DC",
"answer2": "AF and BC",
"answer3": "BC and CD",
"correct_answer": 1,
"skill_id": 119,
"difficulty_id": 2,
"explanation": "On the square grid, AB and DC have the same gradient (same horizontal and vertical step), so they are parallel.",
"hints": ["Parallel lines have the same slope on the grid.", "Compare the rise/run of each line against the grid squares."],
"source": "Nan Hua 2025 P6 Prelim Q4",
"image_needed": true,
"image_options": false,
"image_file": "q4.png",
"image_page": 3,
"image_bbox": [0.24, 0.11, 0.56, 0.32],
"image_loc": "square grid with points A, B, C, D, E, F joined by lines, below the question",
"notes": "Key: option 2 -> index 1."
},
{
"n": 5,
"type_id": 1,
"question": "AOB, POQ and XOY are straight lines.
Which of the following is true?",
"answer0": "∠AOY = ∠XOQ",
"answer1": "∠XOB = ∠YOQ",
"answer2": "∠AOX = ∠YOQ",
"answer3": "∠POY = ∠XOQ",
"correct_answer": 3,
"skill_id": 119,
"difficulty_id": 2,
"explanation": "Vertically opposite angles formed by two straight lines crossing at O are equal. ∠POY and ∠XOQ are vertically opposite, so ∠POY = ∠XOQ.",
"hints": ["Vertically opposite angles are equal.", "Identify which pairs are formed by the same two straight lines."],
"source": "Nan Hua 2025 P6 Prelim Q5",
"image_needed": true,
"image_options": false,
"image_file": "q5.png",
"image_page": 3,
"image_bbox": [0.3, 0.48, 0.62, 0.64],
"image_loc": "three straight lines crossing at point O, with A, P, X, B, Q, Y labelled",
"notes": "Key: option 4 -> index 3."
},
{
"n": 6,
"type_id": 1,
"question": "The figure is made up of four identical right-angled triangles and a square.
What percentage of the figure is shaded?",
"answer0": "25%",
"answer1": "37.5%",
"answer2": "60%",
"answer3": "75%",
"correct_answer": 0,
"skill_id": 110,
"difficulty_id": 2,
"explanation": "The figure is the square plus four identical right-angled triangles. The shaded portion is one triangle on each side; the shaded triangles together make up 25% of the whole figure.",
"hints": ["Find the area of one triangle and the square in equal units.", "Compare total shaded area to the whole figure area."],
"source": "Nan Hua 2025 P6 Prelim Q6",
"image_needed": true,
"image_options": false,
"image_file": "q6.png",
"image_page": 4,
"image_bbox": [0.6, 0.1, 0.86, 0.2],
"image_loc": "top-right of page: a square flanked by four right-angled triangles, partly shaded",
"notes": "Key: option 1 -> index 0."
},
{
"n": 7,
"type_id": 1,
"question": "The duration of a movie is 1h 40 min. The movie ended at 5.30 p.m. What time did the movie begin?",
"answer0": "03 50",
"answer1": "07 10",
"answer2": "15 50",
"answer3": "19 10",
"correct_answer": 2,
"skill_id": 116,
"difficulty_id": 2,
"explanation": "5.30 p.m. = 1730. Subtract 1h 40min: 1730 - 1h 40min = 1550. In 24-hour time the movie began at 15 50.",
"hints": ["Convert 5.30 p.m. to 24-hour time (1730).", "Subtract 1 h 40 min."],
"source": "Nan Hua 2025 P6 Prelim Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"image_page": null,
"image_bbox": null,
"image_loc": null,
"notes": "Key: option 3 -> index 2."
},
{
"n": 8,
"type_id": 1,
"question": "Arrange these distances from the longest to the shortest.
\\(1\\dfrac{1}{4}\\) km, 1 km 40 m, 1.3 km",
"answer0": "1 km 40 m, 1.3 km, \\(1\\dfrac{1}{4}\\) km",
"answer1": "1.3 km, \\(1\\dfrac{1}{4}\\) km, 1 km 40 m",
"answer2": "\\(1\\dfrac{1}{4}\\) km, 1.3 km, 1 km 40 m",
"answer3": "\\(1\\dfrac{1}{4}\\) km, 1 km 40 m, 1.3 km",
"correct_answer": 1,
"skill_id": 113,
"difficulty_id": 2,
"explanation": "Convert to km: 1 1/4 km = 1.25 km, 1 km 40 m = 1.04 km, 1.3 km = 1.3 km. Longest to shortest: 1.3 km, 1.25 km (1 1/4 km), 1.04 km (1 km 40 m).",
"hints": ["Express every distance in km.", "1 km 40 m = 1.040 km; 1 1/4 km = 1.250 km."],
"source": "Nan Hua 2025 P6 Prelim Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"image_page": null,
"image_bbox": null,
"image_loc": null,
"notes": "Key: option 2 -> index 1. MCQ kept because options contain a fraction (1 1/4 km)."
},
{
"n": 9,
"type_id": 1,
"question": "The pie chart shows how Xueli spent her weekly allowance from Monday to Friday in a particular week.
Which of the following bar graphs represent the data shown in the pie chart?",
"answer0": "Bar graph 1",
"answer1": "Bar graph 2",
"answer2": "Bar graph 3",
"answer3": "Bar graph 4",
"correct_answer": 0,
"skill_id": 130,
"difficulty_id": 2,
"explanation": "From the pie chart Fri is the largest sector, Mon and Tue are the smallest, Wed and Thu are in between. The bar graph that matches these relative sizes (smallest Mon/Tue, largest Fri) is graph 1.",
"hints": ["Order the sectors of the pie chart from smallest to largest.", "Match the bar heights to that order."],
"source": "Nan Hua 2025 P6 Prelim Q9",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 5,
"image_bbox": [0.32, 0.13, 0.56, 0.3],
"image_loc": "pie chart (top) with Mon-Fri sectors; four candidate bar graphs labelled (1)-(4) below",
"notes": "Key: option 1 -> index 0. The four options are bar-graph pictures (image_options=true); crop pie chart for stem and each bar graph as q9_opt0..3."
},
{
"n": 10,
"type_id": 1,
"question": "A book costs $b more than a pen. The total cost of a book and 3 pens is $20. Find the cost of a pen.",
"answer0": "\\(\\$\\dfrac{20-b}{3}\\)",
"answer1": "\\(\\$(\\dfrac{20}{4}-b)\\)",
"answer2": "$(20 - 3b)",
"answer3": "\\(\\$\\dfrac{20-b}{4}\\)",
"correct_answer": 3,
"skill_id": 137,
"difficulty_id": 2,
"explanation": "Let a pen cost $p. A book = $(p + b). Book + 3 pens = (p + b) + 3p = 4p + b = 20, so 4p = 20 - b and p = (20 - b)/4.",
"hints": ["Let a pen = $p; a book = $(p + b).", "Form 4p + b = 20 and solve for p."],
"source": "Nan Hua 2025 P6 Prelim Q10",
"image_needed": false,
"image_options": false,
"image_file": null,
"image_page": null,
"image_bbox": null,
"image_loc": null,
"notes": "Key: option 4 -> index 3. MCQ with algebraic expression options."
},
{
"n": 11,
"type_id": 1,
"question": "The postage rates to two different countries are shown.
Kim sent a letter weighing 35 g to Malaysia and a letter weighing 10 g to Japan. How much did she pay altogether?",
"answer0": "$1.60",
"answer1": "$1.90",
"answer2": "$2.75",
"answer3": "$3.60",
"correct_answer": 2,
"skill_id": 115,
"difficulty_id": 3,
"explanation": "Malaysia 35 g: first 20 g = $0.85; remaining 15 g needs 2 lots of 10 g (additional) = 2 x $0.20 = $0.40; total $1.25. Japan 10 g: within first 20 g = $1.50. Altogether $1.25 + $1.50 = $2.75.",
"hints": ["Charge the first 20 g, then each additional 10 g (round up).", "Add the Malaysia and Japan amounts."],
"source": "Nan Hua 2025 P6 Prelim Q11",
"image_needed": true,
"image_options": false,
"image_file": "q11.png",
"image_page": 6,
"image_bbox": [0.23, 0.38, 0.86, 0.48],
"image_loc": "table of postage rates: Mass / Malaysia / Japan, with First 20 g and Every additional 10 g rows",
"notes": "Key: option 3 -> index 2."
},
{
"n": 12,
"type_id": 1,
"question": "In the figure, BCD is an equilateral triangle. ABD is an isosceles triangle with AD = BD and ∠ABD = 46°. Find ∠DCA.",
"answer0": "16°",
"answer1": "37°",
"answer2": "44°",
"answer3": "46°",
"correct_answer": 0,
"skill_id": 120,
"difficulty_id": 3,
"explanation": "AD = BD so ∠DAB = ∠ABD = 46°, giving ∠ADB = 180° - 46° - 46° = 88°. BCD equilateral so ∠BDC = 60° and DC = BD = AD, so triangle ADC is isosceles with ∠ADC = 88° + 60° = 148°; thus ∠DCA = (180° - 148°)/2 = 16°.",
"hints": ["Use the isosceles triangle to find ∠ADB.", "Add ∠BDC = 60° to get ∠ADC, then use isosceles triangle ADC."],
"source": "Nan Hua 2025 P6 Prelim Q12",
"image_needed": true,
"image_options": false,
"image_file": "q12.png",
"image_page": 7,
"image_bbox": [0.28, 0.1, 0.56, 0.27],
"image_loc": "triangle figure with vertices A, B, C, D and 46° marked at B",
"notes": "Key: option 1 -> index 0."
},
{
"n": 13,
"type_id": 1,
"question": "Roy and Jaya finished eating a jar of cookies over 2 days.
On the first day, Roy ate 3 more cookies than Jaya.
On the second day, Roy ate 12 cookies and Jaya ate 8 cookies.
Jaya ate \\(\\dfrac{2}{5}\\) of the total number of cookies. How many cookies did Roy eat?",
"answer0": "15",
"answer1": "21",
"answer2": "23",
"answer3": "35",
"correct_answer": 2,
"skill_id": 137,
"difficulty_id": 3,
"explanation": "Roy ate 3/5 of the total and Jaya 2/5, so Roy ate 1/5 more of the total than Jaya. Roy ate (3 + 12) - 8 = 7 more cookies than Jaya overall, so 1/5 of total = 7, total = 35. Roy ate 3/5 x 35 = 21... checking: Jaya = 2/5 x 35 = 14, Roy = 35 - 14 = 21.",
"hints": ["Roy's total - Jaya's total = the difference in their amounts.", "That difference equals 1/5 of the total; find the total then Roy's 3/5."],
"source": "Nan Hua 2025 P6 Prelim Q13",
"image_needed": false,
"image_options": false,
"image_file": null,
"image_page": null,
"image_bbox": null,
"image_loc": null,
"notes": "Key: option 2 -> index 1 (21). Roy = 3/5 x 35 = 21."
},
{
"n": 14,
"type_id": 1,
"question": "The ratio of the number of girls in Team A to the number of girls in Team B is 2 : 3. The ratio of the number of boys in Team A to the number of boys in Team B is 5 : 3. In Team A, the ratio of the number of girls to the number of boys is 4 : 3. What is the ratio of the number of girls to the number of boys in Team B?",
"answer0": "1 : 1",
"answer1": "2 : 1",
"answer2": "2 : 3",
"answer3": "10 : 3",
"correct_answer": 0,
"skill_id": 135,
"difficulty_id": 3,
"explanation": "Team A girls : boys = 4 : 3. Make girls A = 4u so girls B = 6u (from 2:3). Boys A = 3u so boys B = 3u x 3/5 = 9u/5. Girls B : boys B = 6u : 9u/5 = 30 : 9 = 10 : 3. Re-scaling Team A to girls:boys 4:3 with boys A : boys B = 5:3: let boys A = 5, boys B = 3; then girls A = 5 x 4/3 = 20/3, girls B = 20/3 x 3/2 = 10; girls B : boys B = 10 : 3.",
"hints": ["Link the three ratios through Team A's girls and boys.", "Express girls B and boys B in the same unit, then simplify."],
"source": "Nan Hua 2025 P6 Prelim Q14",
"image_needed": false,
"image_options": false,
"image_file": null,
"image_page": null,
"image_bbox": null,
"image_loc": null,
"notes": "Key: option 4 -> index 3 (10 : 3)."
},
{
"n": 15,
"type_id": 1,
"question": "A sheet of paper in the shape of an isosceles triangle where AB = AC. It is folded along the dotted line BD as shown. Find ∠x.",
"answer0": "58°",
"answer1": "64°",
"answer2": "96°",
"answer3": "100°",
"correct_answer": 2,
"skill_id": 120,
"difficulty_id": 3,
"explanation": "In the original triangle ∠ADB = 80°, so base angle ∠ABD relationships and the 16° fold give ∠x = 96° after folding (the printed key gives option 3).",
"hints": ["Use AB = AC for the base angles.", "Track the angle at A through the fold."],
"source": "Nan Hua 2025 P6 Prelim Q15",
"image_needed": true,
"image_options": false,
"image_file": "q15.png",
"image_page": 8,
"image_bbox": [0.28, 0.42, 0.82, 0.6],
"image_loc": "isosceles triangle ABC with dotted fold line BD (80° marked), arrow, and folded result with 16° and x marked",
"notes": "Key: option 3 -> index 2 (96°)."
},
{
"n": 16,
"type_id": 2,
"question": "Find the value of 35.4 − 9.72.
Ans: [?]",
"answer0": "25.68",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 105,
"difficulty_id": 1,
"explanation": "35.40 - 9.72 = 25.68.",
"hints": ["Line up the decimal points.", "35.40 - 9.72 = 25.68."],
"source": "Nan Hua 2025 P6 Prelim Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"image_page": null,
"image_bbox": null,
"image_loc": null,
"notes": "Key: 25.68."
},
{
"n": 17,
"type_id": 2,
"question": "Round 9652 to the nearest hundred.
Ans: [?]",
"answer0": "9700",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 100,
"difficulty_id": 1,
"explanation": "The tens digit is 5, so round up: 9652 -> 9700.",
"hints": ["Look at the tens digit (5).", "5 or more rounds the hundreds up."],
"source": "Nan Hua 2025 P6 Prelim Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"image_page": null,
"image_bbox": null,
"image_loc": null,
"notes": "Key: 9700."
},
{
"n": 18,
"type_id": 1,
"question": "Find the value of \\(\\dfrac{4}{5} \\div 20\\). Give your answer as a fraction in the simplest form.",
"answer0": "\\(\\dfrac{1}{25}\\)",
"answer1": "\\(\\dfrac{4}{100}\\)",
"answer2": "\\(\\dfrac{1}{5}\\)",
"answer3": "\\(\\dfrac{4}{25}\\)",
"correct_answer": 0,
"skill_id": 107,
"difficulty_id": 2,
"explanation": "4/5 ÷ 20 = 4/5 x 1/20 = 4/100 = 1/25.",
"hints": ["Dividing by 20 is multiplying by 1/20.", "4/100 simplifies to 1/25."],
"source": "Nan Hua 2025 P6 Prelim Q18",
"image_needed": false,
"image_options": false,
"image_file": null,
"image_page": null,
"image_bbox": null,
"image_loc": null,
"notes": "Key: 1/25. Converted to MCQ because the answer is a fraction (FIB must be integer/decimal only)."
},
{
"n": 19,
"type_id": 1,
"question": "After Jenny made a 135° clockwise turn, she ended up facing North. Which direction was she facing at first?",
"answer0": "North-East",
"answer1": "South-East",
"answer2": "South-West",
"answer3": "North-West",
"correct_answer": 2,
"skill_id": 118,
"difficulty_id": 2,
"explanation": "Turning 135° clockwise to end facing North means she started 135° anticlockwise from North, which is South-West.",
"hints": ["Turn 135° anticlockwise from North to find the start direction.", "Each compass step (N, NE, E, ...) is 45°; 135° = three steps."],
"source": "Nan Hua 2025 P6 Prelim Q19",
"image_needed": true,
"image_options": false,
"image_file": "q19.png",
"image_page": 10,
"image_bbox": [0.3, 0.16, 0.6, 0.34],
"image_loc": "8-point compass rose (N, NE, E, SE, S, SW, W, NW)",
"notes": "Key: South-West. Converted to MCQ because the answer is a word/direction (not numeric)."
},
{
"n": 20,
"type_id": 2,
"question": "The figure shows a right-angled triangle. Find the area of the triangle.
Ans: [?] cm²",
"answer0": "54",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 124,
"difficulty_id": 2,
"explanation": "Using base 15 cm... the key uses the perpendicular sides: area = 9 x 12 ÷ 2 = 54 cm².",
"hints": ["Area of a triangle = 1/2 x base x height.", "Use the two perpendicular sides 9 cm and 12 cm: 9 x 12 ÷ 2 = 54."],
"source": "Nan Hua 2025 P6 Prelim Q20",
"image_needed": true,
"image_options": false,
"image_file": "q20.png",
"image_page": 10,
"image_bbox": [0.36, 0.5, 0.66, 0.62],
"image_loc": "right-angled triangle with sides 12 cm, 9 cm and base 15 cm, right angle at the apex",
"notes": "Key: 9 x 12 ÷ 2 = 54 cm²."
},
{
"n": 21,
"type_id": 0,
"question": "Measure and write down
(a) the length of BC.
(b) the size of ∠BAC.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 2,
"explanation": "Measure with a ruler and protractor on the printed figure: BC = 7.4 cm; ∠BAC = 93°.",
"hints": ["Use a ruler for BC.", "Use a protractor for ∠BAC."],
"source": "Nan Hua 2025 P6 Prelim Q21",
"image_needed": true,
"image_options": false,
"image_file": null,
"image_page": 11,
"image_bbox": [0.18, 0.13, 0.66, 0.32],
"image_loc": "triangle ABC with A at top, B lower-left, C right",
"notes": "type_id 0: a physical measure-from-the-printed-figure task (depends on exact print scale), not reliably answerable in-app. Key: (a) 7.4 cm; (b) ∠BAC = 93°."
},
{
"n": 22,
"type_id": 2,
"question": "The first 6 numbers of a number pattern are given.
2, 5, 8, 11, 14, 17, ...
What is the 7th and 20th number in the pattern?
7th number: [?]
20th number: [?]",
"answer0": "20",
"answer1": "59",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 103,
"difficulty_id": 2,
"explanation": "The pattern increases by 3 each time. 7th = 17 + 3 = 20. nth = 2 + (n-1) x 3, so 20th = 2 + 19 x 3 = 59.",
"hints": ["The common difference is 3.", "nth term = 2 + (n-1) x 3."],
"source": "Nan Hua 2025 P6 Prelim Q22",
"image_needed": false,
"image_options": false,
"image_file": null,
"image_page": null,
"image_bbox": null,
"image_loc": null,
"notes": "Key: 7th = 20; 20th = 59."
},
{
"n": 23,
"type_id": 2,
"question": "Siti received a monthly allowance of $120 at the beginning of July. The line graph shows the amount of pocket money she had left at the end of each week of July.
How much did Siti spend in July in total?
Ans: $[?]",
"answer0": "104",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 130,
"difficulty_id": 2,
"explanation": "From the graph she had $16 left at the end. Total spent = weekly drops 40 + 16 + 28 + 20 = 104, i.e. $120 - $16 = $104.",
"hints": ["Read the amount left at the end of week 4 from the graph.", "Total spent = starting $120 - amount left."],
"source": "Nan Hua 2025 P6 Prelim Q23",
"image_needed": true,
"image_options": false,
"image_file": "q23.png",
"image_page": 12,
"image_bbox": [0.18, 0.2, 0.78, 0.46],
"image_loc": "line graph: Amount of money left ($) vs Week 1-4, falling from $80 to about $16",
"notes": "Key: 40 + 16 + 28 + 20 = $104. Same line graph serves Q23 and Q24."
},
{
"n": 24,
"type_id": 2,
"question": "Siti received a monthly allowance of $120 at the beginning of July. The line graph shows the amount of pocket money she had left at the end of each week of July.
(a) In which week did Siti spend the most? Week [?]
(b) How much did she spend in that week? Ans: $[?]",
"answer0": "1",
"answer1": "40",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 130,
"difficulty_id": 2,
"explanation": "The steepest weekly drop is in Week 1: she started with $120 and had $80 left at the end of Week 1, so she spent $120 - $80 = $40, the most of any week.",
"hints": ["The biggest spend is the steepest fall on the graph.", "Week 1: $120 - $80 = $40."],
"source": "Nan Hua 2025 P6 Prelim Q24",
"image_needed": true,
"image_options": false,
"image_file": "q24.png",
"image_page": 12,
"image_bbox": [0.18, 0.2, 0.78, 0.46],
"image_loc": "same line graph as Q23 (Amount of money left vs Week 1-4)",
"notes": "Key: (a) Week 1; (b) 120 - 80 = $40."
},
{
"n": 25,
"type_id": 0,
"question": "A right-angled triangle ABC is drawn on a square grid inside a box. By joining dots on the grid with straight lines, draw a parallelogram PQRS with perimeter twice that of triangle ABC. Parallelogram PQRS must not overlap with triangle ABC.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 119,
"difficulty_id": 2,
"explanation": "Construct a parallelogram on the dot grid whose perimeter is twice the triangle's, not overlapping the triangle. The marked answer shows one valid PQRS in the right portion of the grid.",
"hints": ["Find the perimeter of triangle ABC first.", "Pick parallelogram side lengths giving double that perimeter."],
"source": "Nan Hua 2025 P6 Prelim Q25",
"image_needed": true,
"image_options": false,
"image_file": null,
"image_page": 13,
"image_bbox": [0.15, 0.2, 0.78, 0.45],
"image_loc": "dot-grid box with right-angled triangle ABC drawn at left",
"notes": "type_id 0: a draw-on-the-grid construction task (no single value answer)."
},
{
"n": 26,
"type_id": 2,
"question": "36 is a common multiple of A and B. B is 7 more than A. What is the value of B?
Ans: [?]",
"answer0": "9",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 101,
"difficulty_id": 2,
"explanation": "Factor pairs of 36: 1x36, 2x18, 3x12, 4x9, 6x6. The pair differing by 7 is 2 and 9 (9 - 2 = 7), so A = 2 and B = 9.",
"hints": ["List factor pairs of 36.", "Find the pair where the larger is 7 more than the smaller."],
"source": "Nan Hua 2025 P6 Prelim Q26",
"image_needed": false,
"image_options": false,
"image_file": null,
"image_page": null,
"image_bbox": null,
"image_loc": null,
"notes": "Key: B = 9."
},
{
"n": 27,
"type_id": 1,
"question": "The figure shows a cube. Which two nets are the correct nets of the cube?",
"answer0": "A and B",
"answer1": "A and C",
"answer2": "B and D",
"answer3": "C and D",
"correct_answer": 1,
"skill_id": 126,
"difficulty_id": 2,
"explanation": "Folding each candidate net, nets A and C fold into the cube without overlapping faces; B and D do not.",
"hints": ["Mentally fold each net into a cube.", "A valid net has six faces that fold without overlap."],
"source": "Nan Hua 2025 P6 Prelim Q27",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 14,
"image_bbox": [0.18, 0.08, 0.82, 0.33],
"image_loc": "a cube at top and four candidate nets labelled A, B, C, D",
"notes": "Key: A and C -> index 1. Options are net pictures; provided as four pre-set text option labels rather than the printed answer blanks (single-select MCQ)."
},
{
"n": 28,
"type_id": 2,
"question": "Mr Ang and Mr Lee were 120 km apart. They drove towards each other starting from the same time. Mr Lee's average speed was 10 km/h slower than Mr Ang's average speed. 45 minutes later, they passed each other. What was Mr Ang's average speed?
Ans: [?] km/h",
"answer0": "85",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 133,
"difficulty_id": 3,
"explanation": "Combined speed x 45 min = 120 km. In 45 min (3/4 h) they cover 120 km, so combined speed = 160 km/h. Mr Lee is 10 km/h slower, so 2 x Ang - 10 = 160, Ang = 85 km/h.",
"hints": ["Together they cover 120 km in 45 minutes.", "Combined speed = 160 km/h; Ang + (Ang - 10) = 160."],
"source": "Nan Hua 2025 P6 Prelim Q28",
"image_needed": false,
"image_options": false,
"image_file": null,
"image_page": null,
"image_bbox": null,
"image_loc": null,
"notes": "Key: 85 km/h."
},
{
"n": 29,
"type_id": 2,
"question": "ABCD is a rectangle. AFC and GFE are straight lines. ADEF is a trapezium with AF parallel to DE.
Find the following angles.
(a) ∠AFG [?]°
(b) ∠DAC [?]°",
"answer0": "112",
"answer1": "65",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 120,
"difficulty_id": 3,
"explanation": "(a) AF parallel to DE, so ∠AFE = 180° - 112° = 68°; ∠AFG = 180° - 68° = 112°. (b) ∠GAF = 180° - 112° - 43° = 25°; ∠DAC = 90° - 25° = 65°.",
"hints": ["Use AF parallel to DE for the co-interior/straight-line angles.", "At A the rectangle corner is 90°; subtract ∠GAF."],
"source": "Nan Hua 2025 P6 Prelim Q29",
"image_needed": true,
"image_options": false,
"image_file": "q29.png",
"image_page": 15,
"image_bbox": [0.18, 0.1, 0.6, 0.26],
"image_loc": "rectangle ABCD with diagonal AFC, line GFE, points E, F, G and 43°, 112° marked",
"notes": "Key: (a) ∠AFG = 112°; (b) ∠DAC = 65°."
},
{
"n": 30,
"type_id": 2,
"question": "Find the perimeter of the figure.
Ans: [?] cm",
"answer0": "82",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 123,
"difficulty_id": 2,
"explanation": "The figure is an L/U-shaped region. Adding all the boundary sides: 10 + 10 + 15 + 15 + 4 + 4 + 12 + 12 = 82 cm.",
"hints": ["Add up every side along the boundary.", "10 + 10 + 15 + 15 + 4 + 4 + 12 + 12 = 82."],
"source": "Nan Hua 2025 P6 Prelim Q30",
"image_needed": true,
"image_options": false,
"image_file": "q30.png",
"image_page": 15,
"image_bbox": [0.18, 0.55, 0.45, 0.82],
"image_loc": "shaded rectangular frame with an inner notch; marked 10 cm, 3 cm, 12 cm, 4 cm",
"notes": "Key: 10 + 10 + 15 + 15 + 4 + 4 + 12 + 12 = 82 cm."
},
{
"n": 31,
"type_id": 2,
"question": "The full mark for each test is 100. In the first 4 tests, Ali scored an average of 68 marks. He wants to increase his average test score to 74 marks. How many marks must he score for the 5th test?
Ans: [?]",
"answer0": "98",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 128,
"difficulty_id": 2,
"explanation": "First 4 tests total = 68 x 4 = 272. Required total over 5 tests = 74 x 5 = 370. 5th test = 370 - 272 = 98.",
"hints": ["Total of first 4 = average x 4.", "Required 5-test total = 74 x 5; subtract."],
"source": "Nan Hua 2025 P6 Prelim P2 Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"image_page": null,
"image_bbox": null,
"image_loc": null,
"notes": "Key: 98."
},
{
"n": 32,
"type_id": 2,
"question": "Jane spent \\(\\dfrac{3}{5}\\) of her money on a pair of shoes. She then spent $5 more than \\(\\dfrac{1}{4}\\) of the remainder on a dress. The dress cost $35. How much money did she have at first?
Ans: $[?]",
"answer0": "300",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 109,
"difficulty_id": 3,
"explanation": "Remainder after shoes = 2/5. Dress = 1/4 of remainder + $5 = $35, so 1/4 of remainder = $30, remainder = $120... using the key's units: 1/10 of total + $5 = $35, so 1/10 = $30, total = 1 -> $300.",
"hints": ["After shoes, 2/5 remains; the dress is 1/4 of that plus $5.", "1/4 of the remainder = $30; scale up to the whole."],
"source": "Nan Hua 2025 P6 Prelim P2 Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"image_page": null,
"image_bbox": null,
"image_loc": null,
"notes": "Key: $300."
},
{
"n": 33,
"type_id": 0,
"question": "The dotted line is the line of symmetry. Complete the figure to make it symmetric by shading the least number of squares.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 121,
"difficulty_id": 2,
"explanation": "Reflect each already-shaded square across the diagonal line of symmetry and shade its mirror image; the marked answer shows the completed symmetric pattern.",
"hints": ["Reflect each shaded square across the dotted line.", "Shade only the mirror images that are not already shaded."],
"source": "Nan Hua 2025 P6 Prelim P2 Q3",
"image_needed": true,
"image_options": false,
"image_file": null,
"image_page": 17,
"image_bbox": [0.3, 0.12, 0.66, 0.36],
"image_loc": "square grid with a diagonal dotted line of symmetry and some squares shaded",
"notes": "type_id 0: shade-to-complete-symmetry task (no single value answer)."
},
{
"n": 34,
"type_id": 2,
"question": "The figure shows a cuboid container which is partially filled to a height of 5 cm. To fill it completely, 1386 cm³ of water must be added. What is the height of the container?
Ans: [?] cm",
"answer0": "12",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 127,
"difficulty_id": 2,
"explanation": "Base area = 18 x 11 = 198 cm². Remaining height = 1386 ÷ 198 = 7 cm. Total height = 5 + 7 = 12 cm.",
"hints": ["Volume to add ÷ base area = remaining height.", "Add the 5 cm already filled."],
"source": "Nan Hua 2025 P6 Prelim P2 Q4",
"image_needed": true,
"image_options": false,
"image_file": "q34.png",
"image_page": 17,
"image_bbox": [0.18, 0.46, 0.62, 0.66],
"image_loc": "cuboid container partly filled (5 cm), base 18 cm by 11 cm, full height marked ?",
"notes": "Key: 1386 ÷ 18 ÷ 11 = 7; 7 + 5 = 12 cm."
},
{
"n": 35,
"type_id": 2,
"question": "Alice took 60 minutes to walk from Point A to Point B, which was 3500 m apart. In the same amount of time, she could run 7500 m from Point B to Point C. What is her average speed from Point A to Point C, in km/h?
Ans: [?] km/h",
"answer0": "5.5",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 133,
"difficulty_id": 3,
"explanation": "Total distance = 3500 + 7500 = 11000 m. Total time = 60 + 60 = 120 min = 2 h. Average speed = 11000 m ÷ 2 h = 5500 m/h = 5.5 km/h.",
"hints": ["Add both distances and both times.", "Convert metres and minutes to km and hours."],
"source": "Nan Hua 2025 P6 Prelim P2 Q5",
"image_needed": true,
"image_options": false,
"image_file": "q35.png",
"image_page": 18,
"image_bbox": [0.18, 0.18, 0.78, 0.27],
"image_loc": "straight line A--B--C with 3500 m (A to B) and 7500 m (B to C) marked",
"notes": "Key: 5.5 km/h."
},
{
"n": 36,
"type_id": 2,
"question": "Marbles were packed into three bags. Bag A contained 15n marbles. Bag A had three times as many marbles as Bag B. Bag C had 5 more marbles than Bag B. There were 75 marbles in Bag C. Find the value of n.
Ans: [?]",
"answer0": "14",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 137,
"difficulty_id": 2,
"explanation": "Bag A = 15n, Bag B = 15n ÷ 3 = 5n. Bag C = Bag B + 5 = 5n + 5 = 75, so 5n = 70 and n = 14.",
"hints": ["Bag B = Bag A ÷ 3 = 5n.", "Bag C = 5n + 5 = 75; solve for n."],
"source": "Nan Hua 2025 P6 Prelim P2 Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"image_page": null,
"image_bbox": null,
"image_loc": null,
"notes": "Key: n = 14."
},
{
"n": 37,
"type_id": 2,
"question": "At an event, there was a total of 1446 boys and girls at first. During the break, 20 boys and \\(\\dfrac{3}{8}\\) of the girls went home. The number of girls remaining was \\(\\dfrac{1}{3}\\) the number of boys remaining. What was the difference in the number of boys and girls at first?
Ans: [?]",
"answer0": "454",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 137,
"difficulty_id": 3,
"explanation": "Let boys at first = 15n units arrangement per key: 15n + 20 + 8n = 1446 gives 23n = 1426, n = 62. Difference at first = (15n + 20) - 8n = 7n + 20 = 7 x 62 + 20 = 454.",
"hints": ["Set up units so girls remaining = 1/3 of boys remaining.", "Use the total 1446 to find the unit, then the difference."],
"source": "Nan Hua 2025 P6 Prelim P2 Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"image_page": null,
"image_bbox": null,
"image_loc": null,
"notes": "Key: difference = 454."
},
{
"n": 38,
"type_id": 2,
"question": "The amount of money Bala had was 60% that of Alan's.
(a) Alan had $52. How much did Bala have? Ans: $[?]
(b) After receiving some money from his mother, Bala's amount of money increased by 20%. By what percentage must Alan's money decrease so that they have the same amount of money? Ans: [?]%",
"answer0": "31.20",
"answer1": "28",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 111,
"difficulty_id": 3,
"explanation": "(a) Bala = 60% x $52 = $31.20. (b) Bala after +20% = $31.20 x 1.2 = $37.44. Alan must drop from $52 to $37.44: decrease = ($52 - $37.44) / $52 = $14.56 / $52 = 28%.",
"hints": ["(a) 60% of $52.", "(b) Find Bala's new amount, then the percentage Alan must fall to reach it."],
"source": "Nan Hua 2025 P6 Prelim P2 Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"image_page": null,
"image_bbox": null,
"image_loc": null,
"notes": "Key: (a) $31.20; (b) 28%."
},
{
"n": 39,
"type_id": 2,
"question": "The bar graph shows the number of cars sold at 4 different shops, A, B, C and D respectively. The bar for Shop C is not drawn.
(a) The number of cars sold at Shop C was twice the number of cars sold at Shop A. How many cars were sold at Shop C? Ans: (a) [?]
(b) Shop E sold 175 fewer cars than the total number of cars sold by Shops A, B and D. How many cars did Shop E sell? Ans: (b) [?]",
"answer0": "170",
"answer1": "150",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 130,
"difficulty_id": 2,
"explanation": "(a) Shop A sold 85, so Shop C = 2 x 85 = 170. (b) A + B + D = 85 + 100 + 140 = 325; Shop E = 325 - 175 = 150.",
"hints": ["Read Shop A, B and D heights from the graph.", "(a) double Shop A; (b) total of A, B, D minus 175."],
"source": "Nan Hua 2025 P6 Prelim P2 Q9",
"image_needed": true,
"image_options": false,
"image_file": "q39.png",
"image_page": 21,
"image_bbox": [0.18, 0.13, 0.7, 0.42],
"image_loc": "bar graph of cars sold at shops A, B, C, D (axis 0-200); bar C not drawn",
"notes": "Key: (a) 170; (b) 150. Shop A = 85, B = 100, D = 140 read from graph."
},
{
"n": 40,
"type_id": 2,
"question": "Tracy had five more 50-cent coins than 20-cent coins. After she used eight 50-cent coins, the value of the 50-cent coins is $6.30 more than the value of 20-cent coins. How many coins did she have at first?
Ans: [?]",
"answer0": "57",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 137,
"difficulty_id": 3,
"explanation": "Let 20-cent coins = x, so 50-cent coins = x + 5. After using 8: 50-cent coins = x - 3. Value diff: 0.50(x - 3) - 0.20x = 6.30. The key gives x = 26, so coins at first = 26 + (26 + 5) = 57.",
"hints": ["Let the number of 20-cent coins be x; 50-cent = x + 5.", "Form the value equation after removing 8 fifty-cent coins."],
"source": "Nan Hua 2025 P6 Prelim P2 Q10",
"image_needed": false,
"image_options": false,
"image_file": null,
"image_page": null,
"image_bbox": null,
"image_loc": null,
"notes": "Key: 26 twenty-cent coins; total at first 26 + 31 = 57 coins."
},
{
"n": 41,
"type_id": 1,
"question": "In the figure, a square, a right-angled triangle, and a circle with centre O overlap one another. The ratio of the area of the square to the area of the circle to the area of the triangle is 10 : 8 : 7.
(a) Find the ratio of the shaded area of the figure to the unshaded area of the figure. Give your answer in the simplest form.",
"answer0": "13 : 6",
"answer1": "6 : 13",
"answer2": "10 : 8",
"answer3": "7 : 6",
"correct_answer": 0,
"skill_id": 124,
"difficulty_id": 3,
"explanation": "Unshaded = the circle overlap = 8 x 3/4 = 6 units (per key). Total of the three areas = 10 + 8 + 7 = 25 units. Shaded = 25 - 6 - 6 = 13. So shaded : unshaded = 13 : 6.",
"hints": ["Total area ratio sums to 10 + 8 + 7 = 25.", "Subtract the unshaded (overlap) portions."],
"source": "Nan Hua 2025 P6 Prelim P2 Q11",
"image_needed": true,
"image_options": false,
"image_file": "q41.png",
"image_page": 23,
"image_bbox": [0.26, 0.13, 0.66, 0.34],
"image_loc": "overlapping square, right-angled triangle and circle with centre O, partly shaded",
"notes": "Key: (a) 13 : 6. MCQ because the answer is a ratio. Part (b) recorded separately as n=42."
},
{
"n": 42,
"type_id": 2,
"question": "In the figure, a square, a right-angled triangle, and a circle with centre O overlap one another. The ratio of the area of the square to the area of the circle to the area of the triangle is 10 : 8 : 7. The ratio of the shaded area to the unshaded area is 13 : 6.
Given that the unshaded area of the figure is 86.4 cm², find the area of the triangle.
Ans: [?] cm²",
"answer0": "100.8",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 124,
"difficulty_id": 3,
"explanation": "Unshaded = 6 units = 86.4 cm², so 1 unit = 86.4 ÷ 6 = 14.4 cm². The triangle is 7 units: 14.4 x 7 = 100.8 cm².",
"hints": ["Find the value of 1 unit from the unshaded area.", "Triangle = 7 units."],
"source": "Nan Hua 2025 P6 Prelim P2 Q11",
"image_needed": true,
"image_options": false,
"image_file": "q41.png",
"image_page": 23,
"image_bbox": [0.26, 0.13, 0.66, 0.34],
"image_loc": "same overlapping square/triangle/circle figure as Q41",
"notes": "Key: (b) 86.4 ÷ 6 = 14.4; 14.4 x 7 = 100.8 cm². This is part (b) of Paper 2 Q11."
},
{
"n": 43,
"type_id": 2,
"question": "The figure is made up of two identical parallelograms, ABCD and CFGH. ∠ABD is twice the size of ∠DBC.
(a) Find ∠BDC. Ans: (a) [?]°
(b) Find ∠CDF. Ans: (b) [?]°",
"answer0": "84",
"answer1": "33",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 120,
"difficulty_id": 3,
"explanation": "(a) ∠BAD = ∠BCD = 54° (the 54° at A in the parallelogram). ∠ABC = 180° - 54° = 126°; ∠DBC = 126° ÷ 3 = 42°; ∠BDC = 180° - 54° - 42° = 84°. (b) ∠CDF = (180° - 60° - 54°) ÷ 2 = 33°.",
"hints": ["Use parallelogram angle properties and ∠ABD = 2∠DBC.", "(b) Use the 60° at C and angle sum in the relevant triangle."],
"source": "Nan Hua 2025 P6 Prelim P2 Q12",
"image_needed": true,
"image_options": false,
"image_file": "q43.png",
"image_page": 24,
"image_bbox": [0.18, 0.1, 0.7, 0.27],
"image_loc": "two identical parallelograms ABCD and CFGH joined, with 54° at A and 60° at C marked",
"notes": "Key: (a) ∠BDC = 84°; (b) ∠CDF = 33°."
},
{
"n": 44,
"type_id": 0,
"question": "The following pie charts show the sales of four different flavours of ice-cream in two shops (Shop A and Shop B).
Each of the statements below is either true, false or not possible to tell from the information given. For each statement, put a tick to indicate your answer.
(a) Shop B sold more Orange-flavoured ice-cream than Shop A.
(b) Given that both shops sold the same number of Lemon-flavoured ice-cream, Shop A sold more ice-cream in total compared to Shop B.
(c) Given that Shop A sold 40 Lemon-flavoured ice-cream, Shop A sold a total of 120 ice-cream.
(d) Given that Shop A sold 8 more Mint-flavoured ice-cream than Shop B, the ratio of the number of Mint-flavoured ice-cream sold to the number of Nutella-flavoured ice-cream sold is 2 : 9.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 130,
"difficulty_id": 3,
"explanation": "Tick-table from the pie charts. (a) Not possible to tell; (b) True; (c) True; (d) True.",
"hints": ["Decide each statement from the angles/data shown in the two pie charts.", "Mark True / False / Not possible to tell."],
"source": "Nan Hua 2025 P6 Prelim P2 Q13",
"image_needed": true,
"image_options": false,
"image_file": null,
"image_page": 25,
"image_bbox": [0.18, 0.12, 0.78, 0.3],
"image_loc": "two pie charts (Shop A, Shop B) each with Orange/Lemon/Mint/Nutella sectors; Shop A shows 36, Shop B shows 16",
"notes": "type_id 0: tick-the-box True/False/Not-possible table (no single value answer). Key: (a) Not possible to tell; (b) True; (c) True; (d) True."
},
{
"n": 45,
"type_id": 2,
"question": "Bowls are arranged neatly into 20 stacks of the same height on a shelf in a restaurant. The number of bowls in each stack is the same, and the height of each stack of bowl is 21 cm. An example of how 8 bowls pile up to form one stack is shown.
(a) How many bowls were there on the shelf? Ans: (a) [?]
3 bowls from each stack were removed to form another 12 new stacks. The new height of each stack is now 15 cm tall.
(b) What was the height of each bowl? Ans: (b) [?] cm",
"answer0": "160",
"answer1": "7",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 137,
"difficulty_id": 3,
"explanation": "(a) Each stack has 8 bowls, 20 stacks: 8 x 20 = 160 bowls. (b) Removing 3 bowls drops a stack from 21 cm to 15 cm, a drop of 6 cm for 3 bowls overlap, so 6 ÷ 3 = 2 cm per overlap; per bowl height with the base: 2 x 7 = 14, 21 - 14 = 7 cm.",
"hints": ["(a) bowls per stack x number of stacks.", "(b) The height drop per removed bowl gives the overlap; work back to one bowl's height."],
"source": "Nan Hua 2025 P6 Prelim P2 Q14",
"image_needed": true,
"image_options": false,
"image_file": "q45.png",
"image_page": 26,
"image_bbox": [0.34, 0.14, 0.6, 0.3],
"image_loc": "a stack of 8 bowls with total height 21 cm marked",
"notes": "Key: (a) 8 x 20 = 160 bowls; (b) 7 cm."
},
{
"n": 46,
"type_id": 2,
"question": "The solid is made up of ten cubes (with top, front and side views indicated).
(a) Draw the top view.
(b) Jane painted the whole solid including the base. How many cubes had exactly 4 faces painted? Ans: (b) [?]
(c) What is the minimum number of unit cubes that must be added such that the structure becomes a cube? Ans: (c) [?]",
"answer0": "3",
"answer1": "54",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 126,
"difficulty_id": 3,
"explanation": "(b) 3 cubes have exactly 4 faces painted. (c) Smallest enclosing cube is 4 x 4 x 4 = 64 unit cubes; the solid already has 10, so 64 - 10 = 54 must be added.",
"hints": ["(b) Count cubes exposed on exactly 4 faces.", "(c) Find the smallest cube that encloses the solid (4x4x4), then subtract 10."],
"source": "Nan Hua 2025 P6 Prelim P2 Q15",
"image_needed": true,
"image_options": false,
"image_file": "q46.png",
"image_page": 27,
"image_bbox": [0.28, 0.08, 0.6, 0.24],
"image_loc": "isometric drawing of a solid made of ten unit cubes, with Top/Front/Side views labelled",
"notes": "Part (a) is a draw-the-top-view task (omitted from answers); answers cover (b) = 3 and (c) = 54. Key: (c) 4x4x4 = 64; 64 - 10 = 54."
},
{
"n": 47,
"type_id": 2,
"question": "A shop produces square tiles in two designs. Each tile is made up of 4 quarter-circles. The length of the side of each tile is 20 cm. (Take π = 3.14)
(a) Find the perimeter of the shaded part of Tile B. Ans: (a) [?] cm
Some tiles were laid out on a surface measuring 180 cm by 140 cm, in an alternating manner.
(b) What is the smallest possible shaded area of all the tiles? Ans: (b) [?] cm²",
"answer0": "62.8",
"answer1": "12486",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 125,
"difficulty_id": 3,
"explanation": "(a) Radius = 20 ÷ 2 = 10 cm. Shaded perimeter of Tile B = four quarter-circle arcs = a full circle circumference = 2 x π x 10 = 2 x 3.14 x 10 = 62.8 cm. (b) 140 ÷ 20 = 7 rows, 180 ÷ 20 = 9 columns; using the smaller-shaded (Tile B) tiles where possible, the printed key gives a smallest shaded area of 12486 cm².",
"hints": ["(a) Four quarter-circle arcs make one full circle.", "(b) Count the grid of tiles and minimise the shaded count."],
"source": "Nan Hua 2025 P6 Prelim P2 Q16",
"image_needed": true,
"image_options": false,
"image_file": "q47.png",
"image_page": 28,
"image_bbox": [0.3, 0.12, 0.66, 0.22],
"image_loc": "Tile A and Tile B designs (square with four quarter-circles), side 20 cm marked",
"notes": "Key: (a) 62.8 cm; (b) 12486 cm² (per printed working: 31 pairs x ...). Part (b) working in the printed key is messy; final printed value 12486 cm² used."
},
{
"n": 48,
"type_id": 2,
"question": "The figure is made up of two rectangles, ABFG and BCEF. HXF and BDX are triangles. The perimeter of rectangle ACEG is 90 cm. The ratio of AG : AC = 4 : 5 and X is the midpoint of BF.
(a) Find the length of AG. Ans: (a) [?] cm
(b) Find the area of the shaded part. Ans: (b) [?] cm²",
"answer0": "20",
"answer1": "125",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 124,
"difficulty_id": 3,
"explanation": "(a) AG : AC = 4 : 5, perimeter of rectangle ACEG = 2(AG + AC) = 90, so AG + AC = 45 = 9 units, 1 unit = 5; AG = 4 x 5 = 20 cm. (b) AC = 25 cm; with X the midpoint of BF the shaded triangles total area = 10 x 25 ÷ 2 = 125 cm².",
"hints": ["(a) Half the perimeter = AG + AC = 9 units.", "(b) Use base x height ÷ 2 with the midpoint X."],
"source": "Nan Hua 2025 P6 Prelim P2 Q17",
"image_needed": true,
"image_options": false,
"image_file": "q48.png",
"image_page": 29,
"image_bbox": [0.26, 0.12, 0.74, 0.36],
"image_loc": "two rectangles ABFG and BCEF with points A,B,C,D,E,F,G,H,X; shaded triangles HXF and BDX region",
"notes": "Key: (a) AG = 20 cm; (b) 125 cm²."
}
]
}