# Very Important Basics and Formulae Used in Most Competitive Exams

4.6 out of 5

Language | : | English |

Text-to-Speech | : | Enabled |

Enhanced typesetting | : | Enabled |

Lending | : | Enabled |

File size | : | 4408 KB |

Screen Reader | : | Supported |

Print length | : | 49 pages |

Competitive exams are a common way to assess candidates for jobs, scholarships, and other opportunities. In order to prepare for these exams, it is important to have a strong foundation in the basics of math, science, and other subjects. This article will provide a comprehensive overview of the most important basics and formulae used in various competitive exams.

## Algebra

Algebra is a branch of mathematics that deals with the study of variables and their relationships. It is used in a wide variety of applications, including solving equations, graphing functions, and finding the area and volume of shapes.

**Order of operations:**Parentheses first, followed by exponents, multiplication and division (from left to right),and addition and subtraction (from left to right).**Properties of exponents:***a*^{m}* a^{n}= a^{m+n}*(a*^{m})^{n}= a^{mn}*a*^{0}= 1*a*^{-m}= 1/a^{m}

**Factoring:***(a + b)(a - b) = a*^{2}- b^{2}*(a - b)*^{2}= a^{2}- 2ab + b^{2}*(a + b)*^{2}= a^{2}+ 2ab + b^{2}

**Solving equations:***To solve an equation, isolate the variable on one side of the equation and the constant on the other side.**You can add or subtract the same number from both sides of an equation without changing the solution.**You can multiply or divide both sides of an equation by the same number without changing the solution.*

**Graphing functions:***The graph of a function is a set of all the points (x, y) that satisfy the equation of the function.**To graph a function, plot the points (x, y) that satisfy the equation of the function.**You can use a graphing calculator to graph functions.*

## Trigonometry

Trigonometry is a branch of mathematics that deals with the study of angles and triangles. It is used in a wide variety of applications, including navigation, surveying, and architecture.

**Trigonometric functions:***sine (sin)**cosine (cos)**tangent (tan)**cosecant (csc)**secant (sec)**cotangent (cot)*

**Trigonometric identities:***sin*^{2}(x) + cos^{2}(x) = 1*tan*^{2}(x) + 1 = sec^{2}(x)*sin(x) * cos(x) = 1/2 * sin(2x)*

**Solving trigonometric equations:***To solve a trigonometric equation, isolate the trigonometric function on one side of the equation and the angle on the other side.**You can use the trigonometric identities to solve trigonometric equations.**You can use a calculator to solve trigonometric equations.*

## Calculus

Calculus is a branch of mathematics that deals with the study of change. It is used in a wide variety of applications, including physics, engineering, and economics.

**Limits:***A limit is a value that a function approaches as the input approaches a certain value.**Limits can be used to find the derivative and integral of a function.**You can use L'Hopital's rule to evaluate limits.*

**Derivatives:***A derivative is the rate of change of a function.**Derivatives can be used to find the slope of a tangent line to a graph.**You can use the power rule, product rule, and chain rule to find the derivative of a function.*

**Integrals:***An integral is the area under the curve of a function.**Integrals can be used to find the volume of a solid.**You can use the power rule, substitution rule, and integration by parts to find the integral of a function.*

## Probability

Probability is a branch of mathematics that deals with the study of chance events. It is used in a wide variety of applications, including gambling, insurance, and quality control.

**Probability of an event:***The probability of an event is the likelihood that the event will occur.**The probability of an event is a number between 0 and 1.**The probability of an event occurring is 1 minus the probability of the event not occurring.*

**Conditional probability:***The conditional probability of an event A occurring given that event B has already occurred is the probability of A occurring divided by the probability of B occurring.**Conditional probability can be used to find the probability of a chain of events.*

**Independent events:***Two events are independent if the occurrence of one event does not affect the probability of the other event occurring.**The probability of two independent events occurring is the product of the probabilities of each event occurring.*

This article has provided a comprehensive overview of the most important basics and formulae used in various competitive exams. By understanding these concepts and applying them effectively, you can improve your chances of success on these exams.

4.6 out of 5

Language | : | English |

Text-to-Speech | : | Enabled |

Enhanced typesetting | : | Enabled |

Lending | : | Enabled |

File size | : | 4408 KB |

Screen Reader | : | Supported |

Print length | : | 49 pages |

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4.6 out of 5

Language | : | English |

Text-to-Speech | : | Enabled |

Enhanced typesetting | : | Enabled |

Lending | : | Enabled |

File size | : | 4408 KB |

Screen Reader | : | Supported |

Print length | : | 49 pages |