Tamil Nadu Board Class 9 Mathematics — Flashcards for Quick Revision

A: Yes, this is a well-defined set because given any object, we can clearly decide whether it belongs to this set or not. Rule: All even natural numbers between 1 and 11. Each element can be verified to

A: Step 1: Identify all letters in MATHEMATICS: M-A-T-H-E-M-A-T-I-C-S Step 2: List each letter only ONCE (elements listed only once in a set) Step 3: Result = {M, A, T, H, E, I, C, S} Note: Even though

A: Step 1: Identify the pattern - all odd natural numbers from 1 to 15 Step 2: Express the condition using mathematical notation Step 3: Set-builder form = {x : x is an odd natural number and x ≤ 15} OR

A: Step 1: Use the formula (p+r)/(q+s) where p/q = 1/2 and r/s = 2/3. Step 2: First rational number = (1+2)/(2+3) = 3/5 Step 3: Find another between 1/2 and 3/5 = (1+3)/(2+5) = 4/7 Verification: 1/2 = 0.

A: Step 1: Write 2.945 = 2 + 0.945 Step 2: 0.945 = 945/1000 (move decimal 3 places) Step 3: Convert to mixed number: 2.945 = 2 + 945/1000 = (2 × 1000 + 945)/1000 = 2945/1000 Step 4: Simplify by finding G

A: Step 1: Let x = 0.3555... Step 2: Multiply by 10: 10x = 3.555... Step 3: Multiply by 100: 100x = 35.555... Step 4: Subtract equation 2 from equation 3: 100x - 10x = 35.555... - 3.555... Step 5: 90x =

A: Step 1: Identify a = 2, b = 15, c = 27 Step 2: Find ac = 2 × 27 = 54 Step 3: Find two numbers that multiply to 54 and add to 15 → 6 and 9 Step 4: Split middle term: 2x² + 6x + 9x + 27 Step 5: Group: 2

A: Remainder Theorem: If p(x) is divided by (x - a), remainder = p(a) Here: divisor is (x + 1), so a = -1 Step 1: Substitute x = -1 in f(x) Step 2: f(-1) = (-1)³ + 3(-1)² + 3(-1) + 1 Step 3: f(-1) = -1 +

A: Use Remainder Theorem: To find remainder without performing long division of polynomials Advantage: Quick and efficient method Example: Find remainder when p(x) = 2x⁴ - 6x³ + 3x² + 3x - 2 is divided b