# Algebra for NDA – Tips to Prepare Algebra for NDA 2023 Exam

By BYJU'S Exam Prep

Updated on: September 11th, 2023

**NDA Mathematics Algebra** and Vector Algebra questions asked in the exam account for the maximum weightage from the Mathematics section. So, here are some important preparation tips for the Algebra topics for NDA and commonly used Algebra formulas for the exam. The aspirants must thoroughly read these tips and important NDA Mathematics Algebra formulas shared at the end of this post to understand how to prepare Algebra for NDA exam.

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## Algebra for NDA

The candidate will have to solve 200 questions in 150 minutes. In other words, the candidate will have less than a minute for each question. Let’s see how you can score full marks in the NDA Mathematics Algebra questions of the NDA Exam with these expert preparation tips as well as the best tricks to solve the NDA Algebra questions in minimum time.

**Tip to Prepare Algebra for NDA Exam**

Since NDA Mathematics Algebra accounts for the maximum marks in the section of the exam, it is important that the aspirants prepare this topic thoroughly. Let’s now have a look at how one should prepare and solve Algebra questions for the NDA exam.

**Memorize all Formulae of NDA Mathematics Algebra –**Formulae make up for most parts of algebra and vector algebra for NDA. The best way to remember them is to prepare a revision sheet with all formulae and important points written in order of significance. This will come in handy during last-minute revision.**Solve Previous Year NDA Algebra Questions –**Solving mock papers will give the candidate a general idea of the amount of time to be spent per question and also help the candidate decide if he needs to work on his time management skills. Previous years’ question papers will help the candidate get an idea about the paper pattern and the weightage given to each topic and sub-topic. A regular NDA & NA paper has about 30 to 32 questions from algebra and vector algebra, which amounts to 75 to 80 marks.**Learn Shortcuts and Mental Math to Solve Algebra Topics for NDA –**The candidate should use mental arithmetic and speed calculations as far as possible. This will reduce the amount of written solving that needs to be done and save time. To get a grip on it, the candidate can start applying the concepts of mental arithmetic in his daily activities, such as while purchasing products at a grocery store, etc., and preferably avoid reaching for the calculator. The candidate should try polishing this skill as much as possible since this will not only be useful during the exam but also during later stages of life.

**Basics of NDA Algebra Chapters**

The candidate should remember the basics of every sub-topic under NDA Mathematics Algebra and vector algebra. This will give the candidate an edge over others and help in further preparation and a better understanding of the concepts.

Below are a few instances from various sub-topics that show the basic NDA Mathematics Algebra equations and points involved. The candidate must remember such equations and points to easily understand and solve the sums.

**(A) Logarithms**

Consider the equation 2^{3} = 8. This can be written in log form as log_{2}8 = 3. Here, 3 is the exponent and 2 is the base.

**(B) Complex numbers**

Consider the equation: a + ib. Here, ‘a’ is the real part and ‘b’ is the imaginary part of the equation.

**(C) Quadratic equations**

Here, the basic form of the equation is ax^{2} + bx + c = 0. To find the roots, that is, the value of x, the following equation is used, where -b /a = sum of roots and c/a = product of roots.

**(D) Arithmetic progression (AP)**

An AP is a sequence of numbers where the difference between two consecutive terms is constant. The general form of AP is a, a + d, a + 2d … a + (n-1) d

Where, a = first term; d = common difference, a + (n-1) d = n^{th} or last term

**(E) Geometric progression (GP)**

A GP is a series of numbers where each term, except for the first term, is found by multiplying the previous number by a fixed, non-zero number, called as the common ratio. The common ratio is denoted by r. The formula for the n^{th} or last term is a = ar^{n-1}

**(F) Permutations and Combinations (PnC)**

**(G) Binomial theorem**

The binomial theorem is a faster way to expand a binomial expression that is raised to any power. Its basic formula is:

## Algebra Syllabus for NDA

The sub-topics under the Algebra syllabus for NDA are as follows:

- Concept of set
- Operations on sets
- Cartesian product relation
- Equivalence relation
- Complex numbers and their properties
- Cube root of unity
- Venn diagrams
- De Morgan laws
- Binary system of numbers
- Representation of real numbers on a line
- Modulus
- Argument
- Arithmetic, geometric, and harmonic progression
- Conversion of numbers from decimal to binary system and vice-versa
- Permutations and combinations
- Solution of linear equations
- Quadratic equations with real coefficients
- Binomial theorem and its applications
- Logarithms and their applications.

The sub-topics under vector algebra are:

- 2D and 3D vectors
- magnitude and direction
- Unit and null vectors
- Scalar multiplication of vectors
- Vector Addition

**Reference Books for NDA Mathematics Algebra**

When it comes to mathematics, NCERT books are recommended by a lot of past candidates. We have already shared the NDA Books, which one can refer to for the preparation of both sections of this exam. You can go through it to select the best books for the preparation of the Mathematics section of the NDA exam.

**Important Formulas of NDA Algebra**

The following are some of the most important formulas for NDA Mathematics Algebra:

- a
^{2}– b^{2}= (a – b) (a + b) - (a + b)
^{2}= a^{2}+ 2ab + b^{2} - a
^{2}+ b^{2}= (a – b)^{2}+ 2ab - (a – b)
^{2}= a^{2}– 2ab + b^{2} - (a + b + c)
^{2}= a^{2}+ b^{2}+ c^{2}+ 2ab + 2ac + 2bc - (a – b – c)
^{2}= a^{2}+ b^{2}+ c^{2}– 2ab – 2ac + 2bc - (a + b)
^{3}= [a^{3}+ 3a^{2}b + 3ab^{2}+ b^{3}] or [a^{3}+ b^{3}+ 3ab (a + b)] - (a – b)
^{3}= a^{3}– 3a^{2}b + 3ab^{2}– b^{3} - a
^{3}– b^{3}= (a – b) (a^{2}+ ab + b^{2}) - a
^{3}+ b^{3}= (a + b) (a^{2}– ab + b^{2}) - (a + b)
^{3}= a^{3}+ 3a^{2}b + 3ab^{2}+ b^{3} - (a – b)
^{3}= a^{3}– 3a^{2}b + 3ab^{2}– b^{3} - (a
^{m})(a^{n}) = a^{m+n} - (ab)
^{m}= a^{m}b^{m} - (a
^{m})^{n}= a^{m*n} - a
^{0}= 1 - a
^{m}/ a^{n }= a^{m-n} - a
^{m }= 1/ a^{-m} - a
^{–}^{m }= 1/ a^{m}

That’s all from our side, and we will be providing more useful tips for NDA 1 2023. Stay tuned. Also, check NDA Study Material 2023 exam here.

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