Algebra:
The chapter "Algebra" carrying the weightage of \(40\) marks in the board examination. It covers the concepts like Linear equations in three variables, LCM and GCD of polynomials, rational expressions, square root of polynomials, quadratic equations, graph of variations and quadratic graphs.
| Total marks \(40\) |
Total marks \(= 40\)
|
To prepare well for the board examination, it is necessary to understand the following concepts clearly.
- Linear equation in three variables - To find the value of \(3\) variables in the given system of equations.
- LCM and GCD of polynomials - Finding LCM and GCD of polynomials and relationship between LCM and GCD.
- Rational expression - Simplifying expressions, finding excluded values and perform arithmetic operations in rational expressions.
- Square root of polynomials - Finding square root of polynomials using long division method.
- Quadratic equations - Frame the quadratic equation, finding zeroes and roots of the equation and solving equations using factorization method, completing the square method and formula method.
- Graphs of variation and quadratic graphs - Solving the equation graphically.
| Important Concept (Learning Outcomes) | Expected Question Type | Concept dealt with |
| Linear equation in three variables | Sec C | |
| LCM and GCD of polynomials | Sec A | |
| Rational expressions | Sec A, Sec B, | |
| Square root of polynomials | Sec A, Sec C | |
| Quadratic equation - Finding zeroes, roots, framing the equation and solving the equation and nature of roots. | Sec A, Sec B, Sec C | |
| Graph of variations and quadratic graphs | Sec D |
Let us recall the concepts in Numbers and Sequences:
1. A system of linear equations in three variables will be according to one of the following cases. (i) Unique solution (ii) Infinitely many solutions (iii) No solution.
2. LCM of polynomials: The Least Common Multiple of two or more algebraic expressions is the expression of the lowest degree (or power), divisible by each of them without remainder.
3. GCD of polynomials: GCD of polynomials can be determined using long division method.
4. Relationship between LCM and GCD of polynomials is the product of any two polynomials are equal to the product of their LCM and GCD.
That is, \(f(x) \times g(x) = LCM [f(x), g(x)] \times GCD [f(x), g(x)]\).
5. An expression is called a rational expression if it can be written in the form \(\frac{p(x)}{q(x)}\) where \(p(x)\) and \(q(x)\) are polynomials and \(q(x) \neq 0\). \
6. A value that makes a rational expression (in its lowest form) undefined is called an Excluded value.
7. Square root of polynomials can be determined using factorisation method and long division method.
8. Quadratic equation: Finding zeroes, roots of the quadratic equation.
9. Solving quadratic equation: (i) Factorisation method (ii) Completing the square method (iii) Formula method.