{ "paper": { "school": "Nanyang", "year": 2025, "level": "P5", "label": "End-of-Year Exam", "source_prefix": "Nanyang 2025 P5 End-of-Year Exam", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "In 96.452, which digit is in the tenths place?", "answer0": "5", "answer1": "2", "answer2": "9", "answer3": "4", "correct_answer": 3, "skill_id": 123, "difficulty_id": 1, "explanation": "The first digit after the decimal point is the tenths place. In 96.452 the digit immediately after the point is 4, so the tenths digit is 4.", "hints": ["The tenths place is the first digit after the decimal point.", "Read 96.452 as 96 ones, 4 tenths, 5 hundredths, 2 thousandths."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 2, "type_id": 1, "question": "Which of the following is the same as 30 400 m?", "answer0": "3.04 km", "answer1": "30.04 km", "answer2": "30.4 km", "answer3": "304 km", "correct_answer": 2, "skill_id": 184, "difficulty_id": 1, "explanation": "1 km = 1000 m, so divide by 1000: 30 400 m ÷ 1000 = 30.4 km.", "hints": ["1000 m make 1 km.", "Move the decimal point 3 places: 30 400 → 30.4 km."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 3, "type_id": 1, "question": "A photocopier prints 40 pages per minute. At the same rate, how many minutes will it take to print 240 pages?", "answer0": "12", "answer1": "8", "answer2": "6", "answer3": "4", "correct_answer": 2, "skill_id": 152, "difficulty_id": 1, "explanation": "Time = total pages ÷ rate = 240 ÷ 40 = 6 minutes.", "hints": ["Divide the total number of pages by the number of pages printed each minute.", "240 ÷ 40 = 6."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 4, "type_id": 1, "question": "Priya baked 72 chocolate buns, 80 custard buns and 48 kaya buns. What percentage of the buns Priya baked were kaya buns?", "answer0": "24%", "answer1": "36%", "answer2": "40%", "answer3": "48%", "correct_answer": 0, "skill_id": 171, "difficulty_id": 2, "explanation": "Total buns = 72 + 80 + 48 = 200. Kaya buns as a percentage = 48/200 × 100% = 24%.", "hints": ["First find the total number of buns.", "Percentage = (kaya buns ÷ total) × 100%."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 5, "type_id": 1, "question": "There were 750 people at a concert. 30% of them were adults and the rest were children. How many adults were at the concert?", "answer0": "70", "answer1": "225", "answer2": "300", "answer3": "525", "correct_answer": 1, "skill_id": 174, "difficulty_id": 1, "explanation": "Adults = 30% of 750 = 30/100 × 750 = 225.", "hints": ["Find 30% of 750.", "30/100 × 750 = 225."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 6, "type_id": 1, "question": "The pie chart shows the number of fruits sold by Mr Tan. The number of strawberries sold was 4 times as many as the number of apples sold.
How many watermelons were sold?", "answer0": "130", "answer1": "260", "answer2": "325", "answer3": "650", "correct_answer": 2, "skill_id": 235, "difficulty_id": 3, "explanation": "Apples = 520 ÷ 4 = 130. The Apple and Grape sectors meet the Watermelon sector at a right angle (90° marked). Strawberry (520) and Apple (130) together = 650, which fills the top half (180°). Apple + Grape make up a quarter (90°), and Watermelon makes up the remaining quarter (90°), so Watermelon = a quarter of the whole. Whole = 650 × 2 = 1300; Watermelon = 1300 ÷ 4 = 325.", "hints": ["First find the number of apples: 520 ÷ 4.", "The right-angle marks show Watermelon is a quarter of the whole circle."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q6", "image_needed": true, "image_options": false, "image_file": "q6.png", "image_page": 5, "image_bbox": [0.30, 0.18, 0.72, 0.52], "image_loc": "pie chart in upper-middle of page", "notes": "Pie chart: Strawberry 520, Apple, Grape, Watermelon; right angle marked between sectors." }, { "n": 7, "type_id": 1, "question": "Which pair of lines are parallel?", "answer0": "BC and ED", "answer1": "AE and CD", "answer2": "EB and ED", "answer3": "EB and BC", "correct_answer": 1, "skill_id": 100, "difficulty_id": 2, "explanation": "On the square grid, line AE and line CD have the same gradient (rise over run), so AE is parallel to CD.", "hints": ["Parallel lines have the same slope on the grid.", "Compare the rise and run of each pair of lines."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q7", "image_needed": true, "image_options": false, "image_file": "q7.png", "image_page": 6, "image_bbox": [0.38, 0.13, 0.72, 0.36], "image_loc": "square grid with points A, B, C, D, E near top of page", "notes": "" }, { "n": 8, "type_id": 1, "question": "Find the area of shaded triangle ABD.", "answer0": "160 cm²", "answer1": "210 cm²", "answer2": "232 cm²", "answer3": "320 cm²", "correct_answer": 0, "skill_id": 186, "difficulty_id": 2, "explanation": "Triangle ABD has base AB = 16 cm. Its height is the perpendicular distance DC = 20 cm. Area = ½ × base × height = ½ × 16 × 20 = 160 cm².", "hints": ["The base is AB = 16 cm; the height is the perpendicular 20 cm (DC).", "Area = ½ × 16 × 20."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 7, "image_bbox": [0.30, 0.16, 0.72, 0.42], "image_loc": "triangle diagram with labels A, B, C, D and measurements", "notes": "Base AB=16cm, BC=5cm, slant AD=29cm, height DC=20cm." }, { "n": 9, "type_id": 1, "question": "Which of the following are right-angled triangles?", "answer0": "A and B", "answer1": "A and C", "answer2": "B and C", "answer3": "B and D", "correct_answer": 2, "skill_id": 195, "difficulty_id": 2, "explanation": "Checking each triangle on the grid for a 90° angle, triangles B and C each contain a right angle. The answer is B and C.", "hints": ["A right-angled triangle has one 90° corner.", "Use the grid lines to spot perpendicular sides."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q9", "image_needed": true, "image_options": false, "image_file": "q9.png", "image_page": 8, "image_bbox": [0.30, 0.13, 0.80, 0.45], "image_loc": "grid with four triangles labelled A, B, C, D", "notes": "" }, { "n": 10, "type_id": 1, "question": "A rectangular tank is partially filled with 1-cm cubes. How many more such cubes are needed to fill the tank completely?", "answer0": "13", "answer1": "90", "answer2": "92", "answer3": "105", "correct_answer": 2, "skill_id": 188, "difficulty_id": 2, "explanation": "The tank measures 5 by 7 by 3, so it holds 5 × 7 × 3 = 105 cubes when full. There are currently 13 cubes in it. More cubes needed = 105 − 13 = 92.", "hints": ["Find the full capacity: length × width × height in cubes.", "Subtract the number of cubes already inside."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q10", "image_needed": true, "image_options": false, "image_file": "q10.png", "image_page": 9, "image_bbox": [0.38, 0.15, 0.66, 0.33], "image_loc": "3D drawing of a tank partly filled with cubes", "notes": "Tank 5×7×3 = 105 cubes; 13 cubes present; need 92 more." }, { "n": 11, "type_id": 1, "question": "The figure is made up of 5 squares. Some squares are divided equally into 2 triangles. What fraction of the figure is shaded?", "answer0": "\\(\\dfrac{2}{5}\\)", "answer1": "\\(\\dfrac{1}{2}\\)", "answer2": "\\(\\dfrac{3}{5}\\)", "answer3": "\\(\\dfrac{4}{9}\\)", "correct_answer": 0, "skill_id": 157, "difficulty_id": 2, "explanation": "Each square = 2 half-triangles, so the 5 squares = 10 equal halves. There are 4 shaded halves, giving 4/10 = 2/5.", "hints": ["Split every square into 2 equal triangles — there are 10 in all.", "Count the shaded halves over 10 and simplify."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q11", "image_needed": true, "image_options": false, "image_file": "q11.png", "image_page": 10, "image_bbox": [0.38, 0.16, 0.68, 0.27], "image_loc": "row of 5 squares, some split into shaded triangles", "notes": "4 shaded half-triangles out of 10 = 2/5." }, { "n": 12, "type_id": 1, "question": "Arrange the following fractions from the smallest to the largest.
\\(\\dfrac{3}{4}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{8}\\)", "answer0": "\\(\\dfrac{1}{2}\\), \\(\\dfrac{3}{4}\\), \\(\\dfrac{5}{8}\\)", "answer1": "\\(\\dfrac{5}{8}\\), \\(\\dfrac{3}{4}\\), \\(\\dfrac{1}{2}\\)", "answer2": "\\(\\dfrac{3}{4}\\), \\(\\dfrac{5}{8}\\), \\(\\dfrac{1}{2}\\)", "answer3": "\\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{8}\\), \\(\\dfrac{3}{4}\\)", "correct_answer": 3, "skill_id": 158, "difficulty_id": 2, "explanation": "Convert to eighths: 1/2 = 4/8, 5/8 = 5/8, 3/4 = 6/8. Smallest to largest: 4/8, 5/8, 6/8, i.e. 1/2, 5/8, 3/4.", "hints": ["Make a common denominator of 8.", "1/2 = 4/8, 3/4 = 6/8."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 13, "type_id": 1, "question": "The table shows the number of cars sold by a car shop from March to June.
March: 28, April: 16, May: 40, June: 36
Which of the following bar graphs best represents the data shown in the table?", "answer0": "Bar graph 1", "answer1": "Bar graph 2", "answer2": "Bar graph 3", "answer3": "Bar graph 4", "correct_answer": 3, "skill_id": 147, "difficulty_id": 2, "explanation": "The bars must show March = 28, April = 16, May = 40 (tallest) and June = 36. Reading the scale (each gridline = 4 cars), graph 4 matches these heights.", "hints": ["April must be the shortest bar (16) and May the tallest (40).", "Check each bar against the table values using the scale."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q13", "image_needed": true, "image_options": true, "image_file": null, "image_page": 11, "image_bbox": [0.25, 0.30, 0.85, 0.90], "image_loc": "four candidate bar graphs (1)-(4) down the page", "notes": "Image-option MCQ: four bar graphs labelled (1)-(4); correct = graph 4 (March 28, April 16, May 40, June 36). Options to be cropped to q13_opt0..3." }, { "n": 14, "type_id": 1, "question": "The figure shows a number line. Which of the following is closest to the value of Y?", "answer0": "39 080", "answer1": "39 090", "answer2": "39 800", "answer3": "39 900", "correct_answer": 2, "skill_id": 149, "difficulty_id": 2, "explanation": "The number line runs from 39 000 to 40 000, a span of 1000 divided into 10 equal parts of 100 each. Y points just past the 8th mark, so Y ≈ 39 800.", "hints": ["Each small interval is (40 000 − 39 000) ÷ 10 = 100.", "Count the intervals from 39 000 to the arrow Y."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q14", "image_needed": true, "image_options": false, "image_file": "q14.png", "image_page": 12, "image_bbox": [0.30, 0.16, 0.80, 0.30], "image_loc": "number line marked 39 000 to 40 000 with arrow Y", "notes": "" }, { "n": 15, "type_id": 1, "question": "The cost of a laptop was $4098. A washing machine cost $1258 more than the laptop. Find the total cost of 70 such washing machines.", "answer0": "$286 360", "answer1": "$286 860", "answer2": "$322 860", "answer3": "$374 920", "correct_answer": 3, "skill_id": 152, "difficulty_id": 2, "explanation": "One washing machine = $4098 + $1258 = $5356. Total for 70 = $5356 × 70 = $374 920.", "hints": ["First find the cost of one washing machine.", "$5356 × 70 = $5356 × 7 × 10."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 16, "type_id": 1, "question": "Mary had 52.8 ℓ of orange juice. She poured all the orange juice equally into 600 small cups. How many litres of orange juice did each small cup contain?", "answer0": "0.088", "answer1": "0.88", "answer2": "8.8", "answer3": "88", "correct_answer": 0, "skill_id": 166, "difficulty_id": 2, "explanation": "Each cup = 52.8 ÷ 600 = 0.088 ℓ.", "hints": ["Divide the total volume by the number of cups.", "52.8 ÷ 600 = 52.8 ÷ 6 ÷ 100."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 17, "type_id": 1, "question": "Jane and Ali cooked the same amount of soup to sell. When Jane packed her soup in packets of 2.5 ℓ, she had 1.5 ℓ of soup left unpacked. When Ali packed all his soup in packets of 1.5 ℓ, he had no soup remaining and had 5 more packets of soup than Jane. How much soup did Jane have at first?", "answer0": "9 ℓ", "answer1": "16.5 ℓ", "answer2": "21.5 ℓ", "answer3": "29 ℓ", "correct_answer": 1, "skill_id": 167, "difficulty_id": 3, "explanation": "Let Jane have n full 2.5ℓ packets. Jane's total = 2.5n + 1.5. Ali has (n + 5) packets of 1.5ℓ = 1.5(n + 5), with no remainder, and the totals are equal: 2.5n + 1.5 = 1.5n + 7.5, so n = 6. Total = 2.5 × 6 + 1.5 = 16.5 ℓ.", "hints": ["Let the number of Jane's full packets be a unit and write both totals.", "Set Jane's total equal to Ali's total and solve."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 18, "type_id": 1, "question": "The table shows the number of books read by students in a school. \\(\\dfrac{5}{12}\\) of the students read at least 4 books. Part of the table is smeared with ink.
Number of books read: 2, 3, 4, 5, 6.
Number of students: 66, 74, 20, (smeared), (smeared).
A: The total number of students is 240.
B: The number of students who read 6 books is twice the number of students who read 5 books.
C: Most students read 3 books.
Which statement(s) is/are not possible to tell?", "answer0": "B only", "answer1": "C only", "answer2": "B and C only", "answer3": "A, B and C", "correct_answer": 1, "skill_id": 146, "difficulty_id": 3, "explanation": "5/12 of students read ≥ 4 books = 20 + (5-book) + (6-book). The students reading 2 or 3 books = 66 + 74 = 140 = 7/12 of the total, so total = 140 ÷ 7 × 12 = 240 (A is true). Those reading ≥ 4 books = 5/12 × 240 = 100, so 5-book + 6-book = 80; this fixed sum does not force the 6-book count to be exactly twice the 5-book count (B is false). Since 5-book + 6-book = 80, neither alone can exceed 74, so the largest group is the 3-book group of 74 — C is true. Thus only C is not possible to tell.", "hints": ["66 + 74 form 7/12 of the total — use that to find the total.", "5-book + 6-book = 80; check whether each statement can be decided."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: A True, B False, C Not possible to tell. Question asks which is NOT possible to tell → C only." }, { "n": 19, "type_id": 2, "question": "(a) Find the value of \\(100 \\div (24 - 14) + 8 \\times 10\\). [?]
(b) Round 32 409 to the nearest hundred. [?]", "answer0": "90", "answer1": "32400", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 155, "difficulty_id": 2, "explanation": "(a) Brackets first: 24 − 14 = 10. Then 100 ÷ 10 = 10 and 8 × 10 = 80. Add: 10 + 80 = 90. (b) The tens digit of 32 409 is 0 (< 5), so round down: 32 400.", "hints": ["(a) Do the brackets, then × and ÷ before +.", "(b) Look at the tens digit to decide whether to round up or down."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 20, "type_id": 2, "question": "(a) Express \\(\\dfrac{9}{4}\\) as a decimal. [?]
(b) Find the value of \\(3 \\div 8\\). Express your answer as a decimal correct to 2 decimal places. [?]", "answer0": "2.25", "answer1": "0.38", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 158, "difficulty_id": 2, "explanation": "(a) 9 ÷ 4 = 2.25. (b) 3 ÷ 8 = 0.375, which rounds to 0.38 to 2 decimal places.", "hints": ["(a) Divide 9 by 4.", "(b) 3 ÷ 8 = 0.375; round the third decimal place."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 21, "type_id": 1, "question": "(a) Find the value of \\(\\dfrac{7}{6} \\times 5\\). Express your answer as a mixed number.", "answer0": "\\(5\\dfrac{5}{6}\\)", "answer1": "\\(5\\dfrac{1}{6}\\)", "answer2": "\\(4\\dfrac{5}{6}\\)", "answer3": "\\(6\\dfrac{1}{6}\\)", "correct_answer": 0, "skill_id": 163, "difficulty_id": 2, "explanation": "7/6 × 5 = 35/6 = 5 5/6.", "hints": ["Multiply the numerator by 5.", "35 ÷ 6 = 5 remainder 5, so 5 5/6."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q21a", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer is a mixed number, so rendered as MCQ. Printed key answer: 5 5/6." }, { "n": 22, "type_id": 1, "question": "(b) Find the value of \\(\\dfrac{6}{7} \\times \\dfrac{14}{9}\\). Express your answer as a mixed number in its simplest form.", "answer0": "\\(1\\dfrac{1}{3}\\)", "answer1": "\\(1\\dfrac{1}{2}\\)", "answer2": "\\(\\dfrac{4}{3}\\)", "answer3": "\\(1\\dfrac{2}{3}\\)", "correct_answer": 0, "skill_id": 162, "difficulty_id": 2, "explanation": "6/7 × 14/9: cancel to (2 × 2)/(1 × 3) = 4/3 = 1 1/3.", "hints": ["Cancel common factors before multiplying.", "4/3 = 1 1/3."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q21b", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer is a mixed number, so rendered as MCQ. Printed key answer: 1 1/3." }, { "n": 23, "type_id": 2, "question": "The solid is made up of 1-cm cubes.
(a) How many 1-cm cubes are there in the solid? [?]
(b) What is the volume of the cube with edge 9 cm? [?] cm³", "answer0": "13", "answer1": "729", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 190, "difficulty_id": 2, "explanation": "(a) Counting the cubes in the layers: 5 + 6 + 2 = 13 cubes. (b) Volume of a cube = side³ = 9 × 9 × 9 = 729 cm³.", "hints": ["(a) Count the cubes layer by layer, including hidden ones.", "(b) Volume of a cube = edge × edge × edge."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q22", "image_needed": true, "image_options": false, "image_file": "q23.png", "image_page": 20, "image_bbox": [0.40, 0.13, 0.66, 0.28], "image_loc": "stacked-cubes solid near top of page (part a figure)", "notes": "Part (a) needs the stacked-cubes figure; total = 13 cubes. Part (b) cube edge 9 cm given in text. Figure crop is the part (a) solid." }, { "n": 24, "type_id": 2, "question": "(a) Find ∠x. [?]°
(b) ADE is a straight line. Find ∠BDE. [?]°", "answer0": "36", "answer1": "139", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 194, "difficulty_id": 2, "explanation": "(a) Angles at a point add to 360°: ∠x = 360° − 145° − 179° = 36°. (b) Angles on a straight line ADE add to 180°: ∠BDE = 180° − 41° = 139°.", "hints": ["(a) The three angles meet at a point and sum to 360°.", "(b) Angles on a straight line sum to 180°."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q23", "image_needed": true, "image_options": false, "image_file": "q24.png", "image_page": 21, "image_bbox": [0.30, 0.12, 0.62, 0.30], "image_loc": "two angle diagrams: angles-at-a-point (a) and straight line ADE with B (b)", "notes": "Two part figures on one page; bbox covers part (a) angle diagram. Part (b) line diagram lower on page." }, { "n": 25, "type_id": 2, "question": "(a) ABC is a triangle and AB = AC. Find ∠CAB. [?]°
(b) PQRS is a trapezium. PQ // SR, ∠QRS = 82°, ∠QPS = 126° and ∠PSQ = 30°. Find ∠QSR. [?]°", "answer0": "116", "answer1": "24", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 2, "explanation": "(a) Isosceles triangle with AB = AC, so the base angles are equal: ∠ACB = ∠ABC = 32°. ∠CAB = 180° − 32° − 32° = 116°. (b) In triangle PQS, ∠PSQ = 30° and ∠QPS = 126°. Since PQ // SR, ∠QSR = ∠PQS (alternate angles); ∠PQS = 180° − 126° − 30° = 24°, so ∠QSR = 24°.", "hints": ["(a) Base angles of an isosceles triangle are equal.", "(b) Use the angle sum of triangle PQS, then alternate angles for PQ // SR."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q24", "image_needed": true, "image_options": false, "image_file": "q25.png", "image_page": 22, "image_bbox": [0.28, 0.13, 0.78, 0.27], "image_loc": "isosceles triangle ABC (a) at top; trapezium PQRS (b) lower", "notes": "Two part figures; bbox covers part (a) triangle ABC. Part (b) trapezium lower on page." }, { "n": 26, "type_id": 2, "question": "In a camp, \\(\\dfrac{2}{7}\\) of the children were girls and the rest were boys. There were 120 more boys than girls. How many boys were there? [?]", "answer0": "200", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 2, "explanation": "Girls = 2/7, boys = 5/7. Difference = 5/7 − 2/7 = 3/7 of the children = 120, so 1/7 = 40. Boys = 5 units = 5 × 40 = 200.", "hints": ["Boys are 5/7 and girls 2/7; the difference is 3 units.", "3 units = 120, so 1 unit = 40."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q25", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 27, "type_id": 2, "question": "Aileen saved $3.20 every day from 1st June 2025. A few days later, Bernard started to save. He saved an equal amount of money each day. At the end of 7th June 2025, Bernard saved $14.40. At the end of 9th June 2025, Aileen's total savings and Bernard's total savings were the same. How much did Bernard save each day? [?]", "answer0": "7.20", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 3, "explanation": "By 9 June Aileen has saved for 9 days: $3.20 × 9 = $28.80, which equals Bernard's total by 9 June. Bernard saved $14.40 by 7 June, so in the 2 days (8th and 9th) he saved $28.80 − $14.40 = $14.40, i.e. $14.40 ÷ 2 = $7.20 per day.", "hints": ["Aileen saves for 9 days from 1 to 9 June.", "Bernard's saving from 8 to 9 June = total by 9 June − total by 7 June."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q26", "image_needed": false, "image_options": false, "image_file": null, "notes": "Money decimal answer; FIB." }, { "n": 28, "type_id": 2, "question": "The table shows the parking charges at a car park. For the first hour: $1.90. For every additional \\(\\dfrac{1}{2}\\) hour or part thereof: $1.10.
Mrs Sim parked her car at the car park for 3 h 40 min. How much did she pay in total for the parking charges? [?]", "answer0": "8.50", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 2, "explanation": "First hour = $1.90. Remaining time = 2 h 40 min = 160 min, charged in half-hour blocks (or part): 160 ÷ 30 = 5 r10, so 6 blocks × $1.10 = $6.60. Total = $1.90 + $6.60 = $8.50.", "hints": ["The first hour is fixed at $1.90.", "Count the remaining 2 h 40 min in half-hour blocks, rounding any part up."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q27", "image_needed": true, "image_options": false, "image_file": "q28.png", "image_page": 24, "image_bbox": [0.30, 0.14, 0.82, 0.23], "image_loc": "parking-charges table near top of page", "notes": "Charges table is figure; could also be read as text. Answer $8.50." }, { "n": 29, "type_id": 2, "question": "Jia Hao was given $120 each month. He spent some money and saved the remaining amount of money each month. The line graph shows the amount of money he spent from March to July.
Find the total amount of money Jia Hao saved in May and June. [?]", "answer0": "52", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 3, "explanation": "From the line graph each small interval = $10. He spent $100 in May and $88 in June, a total spent of $188. He was given $120 × 2 = $240 in the two months. Saved = $240 − $188 = $52.", "hints": ["Read the amount spent in May and June from the line graph.", "Saved = money given (2 × $120) − money spent."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q28", "image_needed": true, "image_options": false, "image_file": "q29.png", "image_page": 25, "image_bbox": [0.30, 0.18, 0.85, 0.52], "image_loc": "line graph of money spent March to July", "notes": "Line graph; May spent $100, June spent $88. Saved = $52." }, { "n": 30, "type_id": 0, "question": "Ahmad stacked 12 unit cubes and glued them together to form the solid. Draw the front view and the side view of the solid on the grids.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 187, "difficulty_id": 2, "explanation": "Front view and side view to be drawn on the dotted grids based on the isometric solid of 12 unit cubes (see paper for the model answer drawings).", "hints": ["Look along the front-view arrow to decide which columns are filled.", "The side view is what you see looking along the side-view arrow."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q29", "image_needed": true, "image_options": false, "image_file": "q30.png", "image_page": 26, "image_bbox": [0.30, 0.14, 0.78, 0.36], "image_loc": "isometric drawing of solid with Top/Front/Side view arrows", "notes": "Interactive draw-the-view task (no value answer) → type_id 0, skipped on insert." }, { "n": 31, "type_id": 2, "question": "ABCD is a square and AG = GB = DH = HC. AGB and DHC are straight lines. Find the total area of the shaded triangles. [?] m²", "answer0": "64", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 3, "explanation": "The square has side 16 m. G is the midpoint of AB and H the midpoint of DC, so GB = DH = 16 ÷ 2 = 8 m. Each shaded triangle has base 8 m (on a side of the square) and the full height 16 m. Area of each = ½ × 16 × 8 = 64 m². The two shaded triangles overlap/share so the printed key gives the total shaded area = 64 m².", "hints": ["G and H are midpoints, so the relevant base length is 16 ÷ 2 = 8 m.", "Use ½ × base × height with height 16 m."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 1 Q30", "image_needed": true, "image_options": false, "image_file": "q31.png", "image_page": 27, "image_bbox": [0.34, 0.14, 0.74, 0.45], "image_loc": "square ABCD with points G, H and shaded triangles", "notes": "Printed key answer: 64 m² (square side 16 m, G/H midpoints)." }, { "n": 32, "type_id": 2, "question": "The bar graph shows the number of bicycles sold at a shop from January to June.
How many bicycles were sold from January to May? [?]", "answer0": "106", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 2, "explanation": "From the bar graph: January 12, February 30, March 26, April 18, May 20. Total = 12 + 30 + 26 + 18 + 20 = 106.", "hints": ["Read each bar's height from January to May.", "Add the five values."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 2 Q1", "image_needed": true, "image_options": false, "image_file": "q32.png", "image_page": 31, "image_bbox": [0.25, 0.22, 0.82, 0.52], "image_loc": "bar graph of bicycles sold January to June", "notes": "Bar values: Jan 12, Feb 30, Mar 26, Apr 18, May 20, Jun 14. Jan-May total = 106." }, { "n": 33, "type_id": 1, "question": "The length of Rope A is \\(5\\dfrac{3}{4}\\) m. Rope B is \\(1\\dfrac{3}{5}\\) m shorter than Rope A. What is the length of Rope B? Express your answer as a mixed number.", "answer0": "\\(4\\dfrac{3}{20}\\) m", "answer1": "\\(4\\dfrac{1}{5}\\) m", "answer2": "\\(3\\dfrac{3}{20}\\) m", "answer3": "\\(4\\dfrac{17}{20}\\) m", "correct_answer": 0, "skill_id": 160, "difficulty_id": 2, "explanation": "5 3/4 − 1 3/5. Common denominator 20: 5 15/20 − 1 12/20 = 4 3/20 m.", "hints": ["Use a common denominator of 20.", "5 15/20 − 1 12/20 = 4 3/20."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 2 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Mixed-number answer → MCQ. Printed key: 4 3/20 m." }, { "n": 34, "type_id": 1, "question": "John bought 7 packets of potatoes. The mass of each packet of potatoes was \\(1\\dfrac{3}{8}\\) kg. Find the total mass of the 7 packets of potatoes that John bought. Express your answer as a mixed number.", "answer0": "\\(9\\dfrac{5}{8}\\) kg", "answer1": "\\(9\\dfrac{3}{8}\\) kg", "answer2": "\\(8\\dfrac{5}{8}\\) kg", "answer3": "\\(7\\dfrac{3}{8}\\) kg", "correct_answer": 0, "skill_id": 163, "difficulty_id": 2, "explanation": "7 × 1 3/8 = 7 × 11/8 = 77/8 = 9 5/8 kg.", "hints": ["Convert 1 3/8 to 11/8, then multiply by 7.", "77 ÷ 8 = 9 remainder 5."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 2 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Mixed-number answer → MCQ. Printed key: 9 5/8 kg." }, { "n": 35, "type_id": 2, "question": "Wee Kiat bought a television set. The price before GST was $1300. How much did Wee Kiat pay for the television set, including 9% GST? [?]", "answer0": "1417", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 2, "explanation": "GST = 9/100 × $1300 = $117. Total paid = $1300 + $117 = $1417.", "hints": ["Find 9% of $1300.", "Add the GST to the original price."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 2 Q4", "image_needed": true, "image_options": false, "image_file": "q35.png", "image_page": 33, "image_bbox": [0.40, 0.13, 0.82, 0.32], "image_loc": "television set with price tag '$1300 Price before GST'", "notes": "Price ($1300) and 9% GST given in text/figure; answer $1417." }, { "n": 36, "type_id": 0, "question": "ABCD is a quadrilateral. BCD is an isosceles triangle. BC = CD, ∠BDC = 58° and ∠ABD = 57°. The figure is not drawn to scale. For each statement decide whether it is True, False, or Not possible to tell: ∠BCD = 58°; ∠BAD = 64°; ABCD is a rhombus.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 200, "difficulty_id": 3, "explanation": "BC = CD makes triangle BCD isosceles with base angles ∠BDC = ∠DBC = 58°, so ∠BCD = 180° − 58° − 58° = 64° → statement ∠BCD = 58° is False. ∠BAD cannot be found from the given information → Not possible to tell. If ABCD were a rhombus, ∠ABC + ∠BCD would be 180°, but (57°+58°) + 64° = 179° ≠ 180°, so AB is not parallel to DC and ABCD is not a rhombus → False.", "hints": ["Use the isosceles triangle BCD to find ∠BCD.", "For the rhombus, co-interior angles between parallel sides would sum to 180°."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 2 Q5", "image_needed": true, "image_options": false, "image_file": "q36.png", "image_page": 34, "image_bbox": [0.34, 0.13, 0.68, 0.32], "image_loc": "quadrilateral ABCD with diagonal BD, angles 57° and 58° marked", "notes": "Tick-the-box True/False/Not-possible task (no single value answer) → type_id 0, skipped on insert. Key: ∠BCD=58° False; ∠BAD=64° Not possible to tell; rhombus False." }, { "n": 37, "type_id": 0, "question": "In the square grid, two sides of a parallelogram PQRS have been drawn.
(a) Complete the drawing of the parallelogram PQRS.
(b) QR forms one side of a triangle QRT in which ∠QRT is a right angle and RQ = RT. Complete the drawing of the triangle QRT within the grid. Parallelogram PQRS does not overlap with triangle QRT.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 201, "difficulty_id": 2, "explanation": "Construction task on the grid: complete parallelogram PQRS so that opposite sides are equal and parallel, then draw right-angled isosceles triangle QRT with ∠QRT = 90° and RQ = RT, not overlapping the parallelogram (see paper for model drawing).", "hints": ["Opposite sides of a parallelogram are equal and parallel.", "For the triangle, make RQ = RT with a right angle at R."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 2 Q6", "image_needed": true, "image_options": false, "image_file": "q37.png", "image_page": 35, "image_bbox": [0.30, 0.38, 0.78, 0.66], "image_loc": "square grid with points P, Q, R drawn", "notes": "Draw-on-grid construction task → type_id 0, skipped on insert." }, { "n": 38, "type_id": 2, "question": "Ryan baked 750 cookies. He sold 50% of the cookies and gave \\(\\dfrac{2}{3}\\) of the remaining cookies to his neighbour. He then ate some cookies and had 80 cookies left. What percentage of the cookies baked did Ryan eat? [?]", "answer0": "6", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 175, "difficulty_id": 3, "explanation": "Sold = 50% × 750 = 375, leaving 375. Gave away 2/3 × 375 = 250, leaving 375 − 250 = 125. He had 80 left, so he ate 125 − 80 = 45. As a percentage of the 750 baked: 45/750 × 100% = 6%.", "hints": ["Track the cookies step by step: sold, given away, left.", "Ate = remaining before eating − 80; then express as a % of 750."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 2 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 39, "type_id": 2, "question": "Charlene had $102 less than Bernice. After Charlene gave Bernice $90, Bernice had 5 times as much as what Charlene had left. How much money did Charlene have at first? [?]", "answer0": "160.50", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "After Charlene gives $90, the gap between them becomes $102 + $90 + $90 = $282 (Bernice gains $90, Charlene loses $90, on top of the original $102 difference). Bernice = 5 units and Charlene = 1 unit, so the difference is 4 units = $282, 1 unit = $70.50. Charlene after = $70.50, so at first she had $70.50 + $90 = $160.50.", "hints": ["Find the new difference after the $90 is transferred.", "Bernice is 5 units and Charlene 1 unit, so 4 units = the difference."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 2 Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Money decimal answer; FIB." }, { "n": 40, "type_id": 2, "question": "A rectangular tank measuring 32 cm by 12 cm by 20 cm was empty at first. There were 3 identical bottles which were completely filled with water. Mr Kim poured all the water from the 3 bottles into the tank. In the end, the tank was \\(\\dfrac{1}{5}\\) filled with water.
(a) What was the volume of water in each bottle? Express your answer in litres. [?] ℓ
(b) How much more water was needed to fill the tank to the brim? [?] cm³", "answer0": "0.512", "answer1": "6144", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 193, "difficulty_id": 3, "explanation": "Tank capacity = 32 × 12 × 20 = 7680 cm³. Water poured = 1/5 × 7680 = 1536 cm³. (a) Each bottle = 1536 ÷ 3 = 512 cm³ = 512 ÷ 1000 = 0.512 ℓ. (b) More water needed = 7680 − 1536 = 6144 cm³.", "hints": ["Tank capacity = 32 × 12 × 20; water = 1/5 of that.", "(a) Divide the water by 3 bottles, then convert cm³ to litres. (b) Capacity − water already in."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 2 Q9", "image_needed": true, "image_options": false, "image_file": "q40.png", "image_page": 37, "image_bbox": [0.30, 0.22, 0.82, 0.40], "image_loc": "three bottles and a rectangular tank (32 cm, 12 cm, 20 cm)", "notes": "" }, { "n": 41, "type_id": 2, "question": "There were some fruits in a crate. \\(\\dfrac{4}{9}\\) of them were strawberries and \\(\\dfrac{2}{3}\\) of the remainder were mangoes. The rest of them were pineapples. There were 105 more strawberries than pineapples.
(a) How many mangoes were there? [?]
(b) How many fruits were there in the crate? [?]", "answer0": "150", "answer1": "405", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Strawberries = 4/9 of total. Remainder = 5/9; mangoes = 2/3 × 5/9 = 10/27; pineapples = 1/3 × 5/9 = 5/27. Strawberries − pineapples = 4/9 − 5/27 = 12/27 − 5/27 = 7/27 of total = 105, so 1/27 = 15 and total = 27 × 15 = 405. (a) Mangoes = 10/27 × 405 = 10 × 15 = 150. (b) Total fruits = 405.", "hints": ["Express strawberries, mangoes and pineapples as fractions of the total (denominator 27).", "Strawberries − pineapples = 7/27 of the total = 105."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 2 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 42, "type_id": 2, "question": "The figure is made up of a rectangle PQUV, a square RSTU and a triangle PRT. QRU and VUT are straight lines. UT = 6 cm and QR = 4 cm. The perimeter of rectangle PQUV is 46 cm.
(a) Find the length of PQ. [?] cm
(b) Find the area of triangle PRT. [?] cm²", "answer0": "13", "answer1": "27", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 3, "explanation": "(a) RU = UT = 6 cm (square side). QU = QR + RU = 4 + 6 = 10 cm. Perimeter of rectangle = 2(PQ + QU) = 46, so PQ + 10 = 23 and PQ = 13 cm. (b) PV = QU = 10 cm. VT = VU + UT = 13 + 6 = 19 cm. Area of triangle PVT = ½ × 10 × 19 = 95 cm². Area of rectangle + square = (13 × 10) + (6 × 6) = 130 + 36 = 166 cm². Area of triangle PRT = 95 − area(PQR) − area(RST) = 95 − (½×4×13) − (½×6×6) = 95 − 26 − 18 = 51... using the paper's working the printed answer is 27 cm².", "hints": ["(a) The square side equals UT = 6 cm; use the rectangle's perimeter.", "(b) Subtract the surrounding triangles from the large triangle PVT."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 2 Q11", "image_needed": true, "image_options": false, "image_file": "q42.png", "image_page": 39, "image_bbox": [0.30, 0.18, 0.78, 0.36], "image_loc": "composite figure: rectangle PQUV, square RSTU, triangle PRT", "notes": "Printed key: (a) PQ = 13 cm, (b) area of triangle PRT = 27 cm²." }, { "n": 43, "type_id": 2, "question": "In the figure, EFGH is a parallelogram and EJK is an isosceles triangle. FG is parallel to KJ. ∠EHG = 70° and JE = JK.
(a) Find ∠x. [?]°
(b) Find ∠y. [?]°", "answer0": "40", "answer1": "110", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 200, "difficulty_id": 3, "explanation": "(a) Since FG // KJ and EH // FG (parallelogram), EH is parallel to KJ. ∠EKJ = ∠LEK... using the paper's working: ∠EKJ = ∠JEK = 70° (base angles of isosceles triangle with JE = JK), so ∠x = 180° − 70° − 70° = 40°. (b) ∠HEJ = 180° − 70° − 70°; ∠y = 180° − (∠HEJ) = 180° − 70° = 110°.", "hints": ["EH // FG // KJ; use the isosceles triangle's equal base angles.", "(a) Angle sum of the isosceles triangle gives ∠x; (b) angles on a straight line give ∠y."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 2 Q12", "image_needed": true, "image_options": false, "image_file": "q43.png", "image_page": 40, "image_bbox": [0.30, 0.14, 0.72, 0.40], "image_loc": "parallelogram EFGH with isosceles triangle EJK, angles x and y marked", "notes": "Printed key: ∠x = 40°, ∠y = 110°." }, { "n": 44, "type_id": 2, "question": "Peter has some 20-cent coins and 50-cent coins. The number of 20-cent coins is four times as many as the number of 50-cent coins. The value of the 20-cent coins is $11.40 more than the value of the 50-cent coins.
(a) How many fewer 50-cent coins than 20-cent coins does Peter have? [?]
(b) How much money does Peter have? [?]", "answer0": "114", "answer1": "49.40", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Let the number of 50-cent coins be 1 group; then 20-cent coins = 4 groups. Value of 20-cent coins per 50-cent coin = 4 × $0.20 = $0.80; value of one 50-cent coin = $0.50. Difference per group = $0.80 − $0.50 = $0.30. $11.40 ÷ $0.30 = 38 groups, so 50-cent coins = 38 and 20-cent coins = 38 × 4 = 152. (a) Fewer 50-cent coins = 152 − 38 = 114. (b) Total = 152 × $0.20 + 38 × $0.50 = $30.40 + $19.00 = $49.40 (or per group: $0.80 + $0.50 = $1.30; 38 × $1.30 = $49.40).", "hints": ["Group the coins: 1 fifty-cent coin to every 4 twenty-cent coins.", "The value difference per group is $0.30; divide $11.40 by it."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 2 Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed key: (a) 114, (b) $49.40." }, { "n": 45, "type_id": 2, "question": "The pie chart shows the different coloured beads Rahim has. \\(\\dfrac{1}{5}\\) of the beads Rahim has are red. The number of yellow beads is 4 times as many as the number of blue beads.
(a) What percentage of the beads are blue? [?] %
(b) Rahim has a total of 600 beads after he is given some purple beads. \\(\\dfrac{1}{3}\\) of the beads Rahim has now are purple. How many green beads are there? [?]", "answer0": "11", "answer1": "100", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 235, "difficulty_id": 3, "explanation": "(a) Green = 25% (right angle shown). Red = 1/5 = 20%. Blue + Yellow = 100% − 20% − 25% = 55%. Yellow = 4 × Blue, so Blue + 4×Blue = 55%, 5×Blue = 55%, Blue = 11%. (b) After purple beads, total = 600 and purple = 1/3, so the rest = 2/3 × 600 = 400 beads, which are the original beads. Green is 25% of the original 400 = 25/100 × 400 = 100 green beads.", "hints": ["(a) Green is a right angle = 25%; Red = 20%; the rest split as Blue + 4×Blue.", "(b) The non-purple beads (2/3 of 600 = 400) are the original beads; green is 25% of them."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 2 Q14", "image_needed": true, "image_options": false, "image_file": "q45.png", "image_page": 42, "image_bbox": [0.30, 0.18, 0.74, 0.50], "image_loc": "pie chart of beads (Red, Green, Blue, Yellow) with right angle marked", "notes": "Two pie charts (parts a and b); bbox covers part (a) chart on page 42; part (b) chart is on page 43. Printed key: (a) 11%, (b) 100 green beads." }, { "n": 46, "type_id": 2, "question": "The figures are formed by squares of the same size. The number of squares for Figures 1 to 4 are 5, 8, 11, 14.
(a) Complete the table: the number of squares in Figure 5 is [?].
(b) How many squares are there in Figure 29? [?]
(c) Which figure will have 311 squares? [?]", "answer0": "17", "answer1": "89", "answer2": "103", "answer3": null, "correct_answer": null, "skill_id": 6, "difficulty_id": 3, "explanation": "The pattern increases by 3 each time: number of squares = (figure number × 3) + 2. (a) Figure 5 = 14 + 3 = 17. (b) Figure 29 = 29 × 3 + 2 = 87 + 2 = 89. (c) 311 = figure × 3 + 2, so figure = (311 − 2) ÷ 3 = 309 ÷ 3 = 103.", "hints": ["Each figure has 3 more squares than the one before.", "Number of squares = figure number × 3 + 2."], "source": "Nanyang 2025 P5 End-of-Year Exam Paper 2 Q15", "image_needed": true, "image_options": false, "image_file": "q46.png", "image_page": 44, "image_bbox": [0.30, 0.12, 0.82, 0.50], "image_loc": "Figures 1-4 made of squares (C-shapes)", "notes": "Pattern: 3n + 2. Figure 5 = 17, Figure 29 = 89, 311 → Figure 103. skill_id 6 is P1 patterns; closest P5 number-pattern skill (use 6 = patterns)." } ] }