Algebra — Flashcards
Tamil Nadu Board · Class 10 · Mathematics
25 flashcards for Algebra (Tamil Nadu Board Class 10 Mathematics) to test yourself on key terms and facts. Sample: "Solve the system of linear equations.
Interactive on Super Tutor
Studying Algebra? Get the full interactive chapter.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for flashcards and more.
Free trial, no card needed.
Solve the system of linear equations: 2x - 3y + z = 2, x + y + z = 6, 3x - y + 2z = 11
Answer
Step 1: Label the equations: (1) 2x - 3y + z = 2, (2) x + y + z = 6, (3) 3x - y + 2z = 11 Step 2: Eliminate z from (1) and (2): From (2): z = 6 - x - y. Substitute into (1): 2x - 3y + (6 - x - y) = 2 …
Find the GCD of 2x³ - 5x² + 5x - 3 and x³ + x² - x + 2 using the Euclidean algorithm
Answer
Step 1: Divide 2x³ - 5x² + 5x - 3 by x³ + x² - x + 2 Step 2: 2x³ - 5x² + 5x - 3 = (x³ + x² - x + 2) × 2 + (-7x² + 7x - 7) Step 3: Remainder = -7(x² - x + 1). Ignore the constant factor, continue with …
Reduce the rational expression (x² - 16)/(x² + 8x + 16) to its lowest form
Answer
Step 1: Factor the numerator: x² - 16 = (x + 4)(x - 4) Step 2: Factor the denominator: x² + 8x + 16 = (x + 4)² Step 3: Write the expression: [(x + 4)(x - 4)]/[(x + 4)²] Step 4: Cancel common factor (x…
When do you use the quadratic formula? Give an example where factorization is difficult.
Answer
Use the quadratic formula x = [-b ± √(b² - 4ac)] / (2a) when: 1) The quadratic equation ax² + bx + c = 0 doesn't factor nicely 2) The roots are irrational or complex 3) Quick factorization is not obvi…
Find the square root of 4x² + 20x + 25 using the factorization method
Answer
Step 1: Recognize this as a perfect square trinomial: 4x² + 20x + 25 Step 2: Check if it fits the pattern (ax + b)²: - First term: (2x)² = 4x² ✓ - Last term: 5² = 25 ✓ - Middle term: 2(2x)(5) = 20x ✓ …
Multiply the rational expressions: (x³/9y²) × (27y/x⁵)
Answer
Step 1: Write the multiplication: (x³/9y²) × (27y/x⁵) Step 2: Multiply numerators and denominators: (x³ × 27y) / (9y² × x⁵) Step 3: Simplify numerical coefficients: 27/9 = 3 Step 4: Simplify variables…
Determine the nature of roots of x² + 2x + 5 = 0 without solving
Answer
Method: Use the discriminant Δ = b² - 4ac Step 1: Identify coefficients: a = 1, b = 2, c = 5 Step 2: Calculate discriminant: Δ = (2)² - 4(1)(5) = 4 - 20 = -16 Step 3: Analyze the discriminant: - If Δ…
Solve (x - 2)(x + 4) = 5 by converting to standard form and using factorization
Answer
Step 1: Expand the left side: (x - 2)(x + 4) = x² + 4x - 2x - 8 = x² + 2x - 8 Step 2: Write in standard form: x² + 2x - 8 = 5 Step 3: Move all terms to left: x² + 2x - 8 - 5 = 0 → x² + 2x - 13 = 0 Ste…
+17 more flashcards
Practise AllFrequently Asked Questions
What are the important topics in Algebra for Tamil Nadu Board Class 10 Mathematics?
How many flashcards are available for Algebra?
How should I revise Algebra for the Tamil Nadu Board Class 10 board exam?
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More resources for Algebra
Practice Quiz
Test yourself with a quick quiz
Important Questions
Exam-style questions with answers
Revision Notes
Key points for last-minute revision
Formula Sheet
The chapter's formulas in one place
Chapter Summary
Understand the chapter at a glance
Concept Maps
See how topics connect
Syllabus
What topics to cover
For serious students
Get the full Algebra chapter — start free.
Quizzes, flashcards, an AI doubt solver and a study plan for Tamil Nadu Board Class 10 Mathematics. Free to start, no card needed.