What are the 6 topics that will help you in Algebra for Class 11 Mathematics ISC, NCERT?
Very often, my students ask me how they should prepare a topic before the exams.
How do they go about studying Algebra? This post tells you exactly what you should be studying. Each of these topics form the foundation of Class 12 Maths. So it is imperative for you to understand each of them well if you want to boost up your math grades in Class 12. These 6 topics is what you should be learning in Algebra for Class 11 Mathematic ISC, NCERT.
The 1st topic is Principle of Mathematical Induction. Here, you will use the first principle of Mathematical Induction to prove various mathematical identities and problems on Divisibility. This is by far, the easiest topic as you follow the same approach in all problems and there are no formulas to memorise.
The second topic which you should learn is Complex numbers. Start with the basic definition of complex numbers and the concept of "i" and its properties. Modulus and Conjugate of complex numbers and representation of a complex number in the Argand plane is important. Learning the polar form of a complex number, that is, writing the complex number in terms of its modulus and amplitude is essential knowledge. You also need to learn how to find the locus of a complex number satisfying a given condition and how to sketch it. This topic concludes with learning how to find the square root of a complex number and learning about the cube roots of unity. Click here for more resources.
The 3rd topic in this series is Quadratic Equations. You start with finding the roots of a quadratic equation using the formula.
Nature of the roots of a quadratic equation: You need to be able to solve problems on this.
There is an important formula on finding the sum of the roots and product of the roots of a quadratic equation. Conversely, given the roots of a quadratic equation, you will have to form the equation.
Then, there are conditions when one of the roots of a quadratic equation is unity or zero or reciprocal of each other or one root is positive and the other negative.
Lastly, the most important topic in this section is Quadratic Inequalities, where you have to solve a quadratic inequality. I strongly recommend the method of intervals here. This method is used extensively in Calculus-Applications of Derivatives. Click here for more!
The 4th topic for you to learn is Permutations and Combinations.
Start with the basic factorial notation and get introduced to the Fundamental Principle of Counting.
Learn what is a permutation and how to calculate it together with properties of permutations. ISC students are advised to learn how to calculate permutations without using a scientific calculator.
Practice umpteen problems on permutations involving seating arrangements, digits, alphabets, check cases when the objects are not different as well.
Circular permutations when the clockwise and anticlockwise order is given.
Moving on to combinations, remember that a permutation mean arrangement and a combination mean selection. Understand the definition of a Combination and how to calculate it. Properties of Combinations are extremely important.
A sound knowledge of Permutations and Combinations stands useful while solving problems on Probability. Practice mixed problems involving Permutations and Combinations as well. Click here for more!
The 5th lesson which follows Permutation and Combinations is Binomial Theorem. Note that you have to learn Permutations and Combinations before learning Binomial Theorem. Click here to learn more!
Learn how to use the Binomial Theorem formula to calculate expansions. Basically, there is only one major formula that you need to learn here. If you have (a-b) , just group the negative sign with the b. Finding the number of terms of a Binomial expansion is also necessary.
Binomial coefficients and the general term of an expansion comes next. Finding the coefficient of a particular term can be done using this formula.
The final topic here is Sequences and Series. You start with understanding the basic difference between a sequence and series.
Arithmetic Progression -its nth term and sum of the first n terms are to be learnt.Number of problems can be worked around this.
Likewise, for a Geometric Progression, learn the nth term and the sum of the 1st n terms.
Sum of the terms of a geometric series upto infinity is also an easy formula for you to remember. Combined problems using AP and GP is also something to prepare for. Click here for more resources.
I have shared a few formulas here.
So how do you go about studying? Do you need help?You can contact me for online tutoring. I have been a teacher for around 3 decades and I can help you ace your maths exams. You can choose between one to one tutoring and group classes. All my students do well in their exams.Would you care to share this piece of advice to your fellow students who might need help in Class 11 Mathematics?
Topic wise tutoring is also provided.
Doubt solving for class 11 and 12 NCERT and ISC is also provided. Inspiring you to learn Mathematics!