Mastering Algebra (for Class 10 Board Exams)

Dear Students,

Algebra is the most important section as it can add a maximum of 23 marks to your total score in mathematics. It has been divided into two sections:

• Quadratic equations
• Arithmetic progressions

Check-list for quadratic equations

• When comparing an equation with standard form ax² + bx + c = 0, always take care of signs of a, b and c. For example, 6x² – 5x = 4can be reduced to 6x² – 5x – 4 = 0. On comparing it with the standard form, we get a = 6, b =-5 and c = -4.
• If the method of obtaining roots is not mentioned in the question and you find it difficult to factorize the equation, then just apply the quadratic formula.
• While solving the equation, be careful about the signs as one wrong entry can make a big difference in the answer.
• If you get the final form of the equation in the form of the identity x² – a², then there are always two equal roots with opposite signs. These are +a and −a. For example, if the reduced form of the equation is x² – 25 = 0, then the roots will +5 and −5.
• Sometimes students write the quadratic formula incorrectly as  . The correct quadratic formula is .
• The conditions for different types of roots of a quadratic equation ax² + bx + c = 0 are as follows:
  • Two distinct real roots, if b² − 4ac > 0 or b² > 4ac
  • Two equal real roots, if b² − 4ac = 0 or b² = 4ac
  • Imaginary roots or no real roots, if b² − 4ac < 0 or b² < 4ac
• In order to solve the word problems, first of all assume the value of the asked quantity as x. After that read the statement step by step and keep forming the equations according to the conditions given. Finally, solve it with any method to get the value of x.

Check-list for arithmetic progressions

• The  nth term of A.P. is given by a_n = a + (n – 1) d.
• The sum of n terms of an A.P. is given by     or        .
• While finding the common difference, remember that the previous term is to be subtracted from the next term.
• Sometimes an A.P. has negative terms, so take care about the signs while finding the common difference or entering values in the formula.
• Most of the mistakes in A.P. problems take place when students get confused between n^th term and sum of n terms. Remember, when in the given question sum is asked for, 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.

Best of luck !