Karnataka Board Class 10 Mathematics — Flashcards
Karnataka Board Class 10 Mathematics flashcards, chapter by chapter — 280 flashcards across 14 chapters. Follows the KSEEB / PUE syllabus.
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- Check the answer — mark the cards you got wrong.
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Chapter-Wise Flashcards — 14 Chapters
Q: Find the prime factorization of 140 and express it as a product of prime powers.
A: Step 1: Divide 140 by smallest prime (2) → 140 ÷ 2 = 70 Step 2: 70 ÷ 2 = 35 Step 3: 35 ÷ 5 = 7 Step 4: 7 is prime Therefore: 140 = 2² × 5 × 7 Answer: 140 = 2² × 5¹ × 7¹
Q: Find HCF and LCM of 96 and 404 using prime factorization method.
A: Step 1: Prime factorization 96 = 2⁵ × 3¹ 404 = 2² × 101¹ Step 2: HCF = Product of lowest powers of common factors Common factor: 2 HCF = 2² = 4 Step 3: LCM = Product of highest powers of all factors L
Q: Verify that HCF × LCM = Product of numbers for 26 and 91.
A: Step 1: Prime factorization 26 = 2¹ × 13¹ 91 = 7¹ × 13¹ Step 2: Find HCF and LCM HCF = 13¹ = 13 (common factor) LCM = 2¹ × 7¹ × 13¹ = 182 Step 3: Verify the relationship HCF × LCM = 13 × 182 = 2366 Pr
Q: In right triangle ABC, if AB = 24 cm, BC = 7 cm, and angle B = 90°, find sin A and cos A.
A: Step 1: Find AC using Pythagoras theorem AC² = AB² + BC² = 24² + 7² = 576 + 49 = 625 AC = √625 = 25 cm Step 2: Apply trigonometric ratios sin A = opposite/hypotenuse = BC/AC = 7/25 = 0.28 cos A = adj
Q: If tan θ = 4/3, find all other trigonometric ratios.
A: Step 1: Draw right triangle where opposite = 4k, adjacent = 3k Step 2: Find hypotenuse using Pythagoras hypotenuse² = (4k)² + (3k)² = 16k² + 9k² = 25k² hypotenuse = 5k Step 3: Calculate all ratios s
Q: Calculate: sin² 30° + cos² 30°
A: Step 1: Recall values from table sin 30° = 1/2 cos 30° = √3/2 Step 2: Square each value sin² 30° = (1/2)² = 1/4 cos² 30° = (√3/2)² = 3/4 Step 3: Add them sin² 30° + cos² 30° = 1/4 + 3/4 = 4/4 = 1 N
Q: Find the zeros of the polynomial p(x) = x² - 5x + 6
A: Step 1: Factor the polynomial. Look for two numbers that multiply to 6 and add to -5. Those are -2 and -3. Step 2: x² - 5x + 6 = (x - 2)(x - 3) Step 3: Set each factor to zero: x - 2 = 0 or x - 3 = 0
Q: Verify the relationship between zeros and coefficients for p(x) = 2x² - 7x + 3
A: Step 1: Find zeros by factoring: 2x² - 7x + 3 = (2x - 1)(x - 3) Zeros: x = 1/2 and x = 3 Step 2: Check sum of zeros: Sum = 1/2 + 3 = 7/2 From formula: -b/a = -(-7)/2 = 7/2 ✓ Step 3: Check product of
Q: If α and β are zeros of x² - 6x + 8, find α + β and αβ without finding the actual zeros
A: Given: p(x) = x² - 6x + 8 Compare with ax² + bx + c where a = 1, b = -6, c = 8 Step 1: Sum of zeros formula: α + β = -b/a = -(-6)/1 = 6 Step 2: Product of zeros formula: αβ = c/a = 8/1 = 8 Answer:
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Where can I find Karnataka Board Class 10 Mathematics Flashcards?
This page has flashcards for 14 chapters of Karnataka Board Class 10 Mathematics for the board exams 2027. Each chapter links to its own page with the full set.
How should I prepare for Karnataka Board Class 10 Mathematics board exams?
Go through the syllabus first, then work chapter by chapter: learn the ideas, practise questions, and revise with notes and flashcards. Leave time at the end to revise every chapter once more under timed conditions.
How do I use flashcards for Karnataka Board Class 10 Mathematics?
Read the question side, answer it in your head, then check. Put the cards you got wrong back into the pile and review them again the next day. Short daily sessions work better than long ones.
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Karnataka Board Class 10