Algebra (Class 10)

Algebra is the most important section as it can add 20 marks to your total score in maths. You need to make a very good strategy for this section.

Algebra has been divided into following two parts:

1. Quadratic equations
2. Arithmetic progressions

When it comes to quadratic equations, there are few things to keep in mind given as follows:

1. When comparing an equation with standard form , always take care of signs of a, b and c. For example can be reduced to . On comparing it with standard form we find that a = 6, b = 5 and c = 4.
2. If the method of obtaining roots is not mentioned in the question and you find it difficult to factorize the equation then do not waste time, just apply the quadratic formula.
3. While solving the equation, be careful about the signs as one wrong entry can make big difference in the answer.
4. If you get the final form of the equation in the form of the identity then there are always two equal roots with opposite signs which are +a and −a. For example, if the reduced form of the equation is as  then the roots will +5 and −5.
5. Sometimes students write the quadratic formula incorrectly as . In the correct formula 2a is denominator for both terms given above. The correct quadratic formula is .
6. Remember the conditions for different types of roots of a quadratic equation ax2 + bx + c = 0, which are as follows:
   1. Two distinct real roots, if b² − 4ac > 0 or b² > 4ac
   2. Two equal real roots, if b² − 4ac = 0 or b² = 4ac
   3. No real roots or imaginary roots if b² − 4ac < 0 or b² < 4ac
7. In order to solve the word problems, first of all assume the value which needs to be find as x. After that read the statement step by step and keep forming the equations according to the conditions given and solve it with any method to find the value of x.

Arithmetic progressions

All of the arithmetic problems are based on the following formulae which are as follows:

1. The  nth term of A.P. is given by aⁿ= a + (n – 1) d.
2. The sum of n terms of an A.P. is given by     or   .

Where a first term, d is common difference and l is the last term of the A.P.

Few of the tips for this section are as follows:

1. While finding the common difference, remember that the previous term is to be subtracted from the next term.
2. Sometimes an A.P. has negative terms, so take care about the signs while finding common difference or entering values in the formula.
3. Most of the mistakes in A.P. problems takes place when students get confused between n^th term and sum of n terms. Remember, when in the given question sum is asked you have to apply the corresponding formula for S_n and when n^th term needs to be find out then apply the formula of  a_n

Apart from this, eat well, take proper rest and keep yourself healthy as a healthy and happy brain can always make a better way out.

All the Best!