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Mathematics is the discipline concerned with the investigation and analysis of structure, order, and relationships. The fundamental techniques for quantifying, evaluating, and characterizing the morphology of an entity have undergone progressive development throughout history. This study examines dimensions such as

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The discipline of mathematics referred to as algebra employs variables as fundamental components for constructing equations with the purpose of resolving numerical issues. Algebra plays a supportive role in the establishment of mathematical foundations. The field of algebra comprises a wide range of mathematical entities, including real numbers, complex numbers, vectors, matrices, and various other mathematical forms. Equations play a crucial role in the realm of algebraic applications. Algebraic reasoning is a fundamental process that entails establishing connections and transforming problems into equations, subsequently solving these equations to get the solution. The topic of this piece aims to analyze the various branches and sub-branches within the field of algebra. 

The term “ratio” is the origin of the term “rational.” Rational numbers are inherently interconnected with the concept of fractions, which represent ratios. In alternative terminology, a numerical value is classified as a rational number if it possesses the property of being expressible as a fraction, whereby both the numerator and denominator are integers. This chapter will focus on the examination of arithmetic operations performed on rational numbers, the exploration of properties inherent to rational numbers, and the depiction of rational numbers on a number line.

The field of mensuration is concerned with the computation of various geometric figures and their corresponding qualities, such as area, length, volume, lateral surface area, and surface area, among others. The material encompasses the essential mathematical equations, the characteristics of various geometric shapes and figures, and the principles of computational concepts. The field of geometry encompasses the study of measuring. Mensuration pertains to the quantitative analysis of the measurements, surface areas, and volumetric properties of diverse two-dimensional and three-dimensional geometric figures. This chapter will focus on the examination of the area and perimeter of the provided geometric figure.

The term “cube” refers to the mathematical operation of raising a number to the power of three. Conversely, a “cube root” denotes the inverse operation, whereby a number is determined that, when raised to the power of three, yields the original number. Alternatively, it might be posited that the cube root of a number of yields a value that, when raised to the power of three, results in the original number, thereby being classified as a perfect cube. This chapter will focus on the concept of cube numbers and their corresponding cube roots. Furthermore, it is worth noting that the concept of cube roots extends beyond perfect cubes to encompass imperfect cubes and decimal numbers.

Algebraic expressions are mathematical assertions that arise from the application of operations such as addition, subtraction, multiplication, division, and others to variables and constants. It is evident that the majority of mathematical issues are presented in verbal form, regardless of whether one is engaged in classroom instruction on algebra or perusing a specific examination.Hence, in order to address these challenges, it becomes necessary to transform verbal word problems into algebraic formulas. The majority of word problems encountered in algebraic contexts consist of concise narratives or scenarios that are derived from real-life occurrences. The remaining phrases consist of concise descriptions similar to those found in mathematical problems. This chapter will focus on the study of mathematical operations performed on algebraic expressions, as well as the identification and utilization of common factors.

Exponents play a crucial role in numerous mathematical procedures. This chapter introduces the concept of exponents and the mathematical calculations associated with them. Given the frequent usage of exponents in various mathematical disciplines, it is imperative to grasp the fundamental principles elucidated in this chapter in order to facilitate comprehension and application in subsequent studies.Exponents play a significant role in the computation of areas within the realm of pre-algebra. Additionally, advanced mathematical disciplines, including algebra, geometry, calculus, and higher mathematics, will rely significantly on these fundamental concepts.

The phenomenon in which two quantities exhibit a consistent ratio is referred to as direct proportion or direct variation. The proportional sign (∝) is utilized as a symbol to represent this concept. In this scenario, the inverse relationship between variables is denoted by the same symbol, despite the reversal of the other variable.Suppose that by increasing your driving speed, you may potentially reduce the time required to reach your intended location. Similarly, an individual engaged in manual work who dedicates additional time to their labor would receive a higher remuneration. In this context, it can be observed that there exists an inverse relationship between time and speed, indicating that these variables are inversely proportionate. Conversely, the relationship between pay and working hours is direct, suggesting a positive correlation between these two factors. To gain a comprehensive understanding of the interdependence of quantities, it is advantageous to engage with the content presented in this chapter, which focuses on direct and inverse proportions.

Comparing quantities involves determining the relationship between two or more quantities. It is a fundamental idea in mathematics that enables us to comprehend the proportions, values, or relative sizes of various quantities. Depending on the context and the kind of values being compared, many formulas and approaches can be used to compare quantities. In this chapter, we are going to discuss ratios and percentages, Buying and selling, Simple and compound interest.

The square root of a number is defined as the factor of the number that, when multiplied by itself, results in the original number. Special exponents encompass both squared values and square roots. Consider the numerical value of 9. When the numeral 3 is multiplied by itself, the outcome is 9. The above expression can be equivalently represented as either 32 or the product of 3 and 3. The mathematical operation that is the inverse of squaring an integer is determining its square root. The product of a number multiplied by itself results in its square value, but the square root of a number can be determined by identifying a number that, when squared, produces the original value. This chapter will examine the characteristics of square numbers, as well as the concepts of repeated subtraction and factorization.

Data processing can be conceptualized as a statistical procedure that serves to enhance the precision and reliability of research data. The concept pertains to the preservation of secrecy, safeguarding, and ensuring the security of the research data. Quantitative data is frequently utilized in several domains for mathematical data processing. The process of performing numerical computations is essential for comprehending and analyzing data and statistical information. The phrase “observations” encompasses all numerical values. The course will provide comprehensive knowledge on the concept of data handling, encompassing its various aspects. Additionally, illustrative examples will be employed to demonstrate effective methods of data representation.


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