Tools to Solve problems in Algebra
In Algebra, word problems and equations related to the word problems are the most common type of questions. Equations can be represented in different forms and they require some tools to bring out the perfect answer!
Methods to Solve Quadratic Equations
The general form of a quadratic equation is ax2+ bx+ c=0, where a = 0 and is an example of a non-linear function.
Given any quadratic equation there are various methods of solving them in order to find their intercepts, vertex and axis of symmetry.
Number, Operation and Quantitative Reasoning
Numbers can be combined through various methods like addition, subtraction, multiplication and division. When using addition and multiplication between numbers, certain rules which have to be followed.
Quadratic Functions
A quadratic function can be represented in multiple ways, one of them being the standard form and the other being the vertex form. Both the equations are helpful in finding the vertex and other details like axis of symmetry and intercepts of the parabola.
It is a group or collection of numbers put together in a fixed format, represented with the ‘square braces -> [ ]’. These numbers are arranged in rows and columns and the numbers present in the braces are called elements of the matrix.
Arithmetic sequences and series
A Sequence is the list of numbers written in a particular order following a pattern. A Series is the sum of the list of the numbers written in the specific order in a sequence. The sequence and series can have numbers extending up till infinity and they are called infinite sequence and infinite series.
Exponential and Logarithmic functions
An exponential function can be defined as function which has a constant base and that base is raised to a power (or exponent). These functions are increasing functions and can give huge numbers as the output. The simplest form of an exponential function is:
Similarity and geometry shape
Similarity: Two objects are similar if the angles one object is equal to the angles of the other and if the sides of one object are in proportion with the sides of the other. It is important to remember that the shape of both the object however remains the same.
Properties and attributes of Functions :
Properties of functions: Functions come under sub-category of Relations. Functions are organized relations where proper order has to be maintained while linking one set to another set. There are different ways of linking one set to another set and the following are the examples!
Rational Functions – A rational function is defined as the function which can be expressed as a ratio of two given polynomials. The polynomial functions can have any highest exponent and it is written in the general form as: