GMAT Algebra Syllabus 2020: Section Wise Details

    If a student is aspiring to become a leader in the corporate world, then the first and foremost action they have to undertake is – getting admission to a reputed business school. An acclaimed institution will not only award the student with skillful knowledge but also proficiency in the concerned subjects. For a student to get into one of those esteemed business schools, they need to crack the GMAT exam with flying colors or some high scores. Now, coming to the content of the GMAT exam – it is one of the most acknowledged entrance exams for MBA throughout the world. The majority of the business schools only accept GMAT and if you are somebody also enrolling for Indian top B-schools then be rest assured, the renowned colleges are accepting GMAT scores too. But the problem arises when it comes to the main GMAT exam. The disposition of the GMAT exam is quite complex. Wondering why?

    Well, the GMAT syllabus has four main categories – analytical writing assessment or AWA, logical reasoning, verbal ability, and lastly quantitative reasoning. Today we are going to clarify the syllabus of the quant section of GMAT with a special focus on the algebra syllabus of GMAT. The GMAT quant section comprises three main divisions – GMAT arithmetic, GMAT geometry, and GMAT algebra. The majority of the student’s favorite part was algebra during high school. GMAT algebra syllabus too, fortunately, houses most of the topics that the students had in their school time. The first step towards a complete study of the GMAT quant section is to go through the syllabus first. Let us discuss the algebra syllabus of GMAT in detail today.

    Algebra: Algebra is a part of mathematics where symbols stand for numbers. Algebra is used to find answers to variables and equations. Letters that are commonly used to solve algebraic problems are – x, y, z, and more. 

    GMAT Algebra: Algebraic Expressions

    Algebraic terms are vital for further understanding of the GMAT algebra syllabus and also form a major part of it. 

    • Variables: they are the symbols that stand for numbers.
    • Constants: they are the values that are stagnant in certain problems.
    • Terms: when constant and variable are singular or clubbed together, they form terms.
    • Algebraic expression: this is the assortment of terms mingled together by the involvement of addition or deduction and forms something like (x + 2), (x – 3c), and (2x –3y).
    • Coefficient: It is a number or symbol that caters as a measure of a property or characteristics.

    Types of expressions in GMAT Algebra:

    1. Monomial: contains only one term like 3x.
    2. Polynomial: it contains more than one term like a2 – b2
    3. Binomial: it is like polynomial and contains two terms like a+b or 3a+6

    Formulas: 

    • (a + b)2 = a2 + 2ab + b2
    • (a - b)2 = a2 - 2ab + b2

    GMAT Algebra: Linear Equations

     One of the most common chapters during school and also in the GMAT algebra syllabus. A linear equation is an algebra equation that comprises an unknown variable and no exponent greater than 1. In its easiest structure, a linear equation is represented as ax + b = y, where x is the variable and a and b are constants.

    Linear Equations: Linear Equations are also termed as first degree equations. Linear equations incorporate variables of first degree only (no quadratic or cubic terms).

    To clear up a linear equation with one unknown, the unknown should be confined to one side of the equation. To further this, one has to carry out a similar mathematical performance on both sides. For example,

    • 5x - 6 = 12
    • 5x = 18
    • x = 18/5

    Linear equations with two unknowns:

    When you are solving x in any question that becomes easy. But when another variable pops up in the question, it will definitely become relatively tougher. That kind of question consists of simultaneous equations. In this time, find the answer for one variable and then substitute it into the other equation.

    • 6x + 4y = 66
    • -2x + 2y = 8

    Our motive is to find a way to remove one of the variables.

    Few points to remember:

    • Study the equations to recognize what terms you can remove through addition or subtraction.
    • Club similar terms and determine
    • Attach the value of one variable into any one of the equations and deal with the other value.

    Number of solutions

    For two linear equations with two anonymous numbers, if the equations are similar, then there are indefinite answers to the sum. If the equations are not the same, then they have either a unique solution or no solution.

    GMAT Algebra: Quadratic equations

    A thorough analysis of the GMAT quant section will result in this topic appearing constantly every year in the exams. The quadratic equation states that it can be penned in the form ax2 + bx + c = 0, where a, b, and c are constants (real numbers) and a ≠ 0, and x is a variable that has to be dealt with. This is a very important topic in the whole GMT algebra syllabus.

    For example, 2x2 + 3x + 2 = 0 is a quadratic equation while 3x + 2 is not a quadratic equation.

    Factoring Method of Solving Quadratic Equation

    The most straightforward method to find an answer to a quadratic equation is to seek to factor the equation into two binomials. It is the procedure of separating an equation into factors (or separate terms) which implies that during the multiplication of autonomous, they result in the original equation. 

    Resolving solutions for the difference of perfect squares

    Root: Root is the answer to the equation such that f(x) = 0. For instance, for the quadratic equation x2 + x - 12 = 0, x = 3 and x = -4 are both roots. Normally, quadratic equations comprise two available solutions.

    Quadratic Formula for answering quadratic equations

    GMAT Algebra: Functions

    Functions are exchanged between two sets of numbers; every single number that one puts into the formula, counters with one possible answer. An algebraic expression can be utilized to procure a function of that particular variable. A function is represented by a letter such as for g along with the variable in the expression.

    For example, the expression x3 - 5x2 + 2 states a function f that can be displayed by f(x) = x3 - 5x2 + 2.

    GMAT Algebra functions

    • The moment a function f(x) is explained, it can be imagined of the variable x as input and f(x) as the coordinating output. In any function, more than one output cannot be accepted. However, it is also to be noted that more than one input will result in one output only.
    • Function: A rule that produces an individual member of one set of numbers into a member of another set.
    • Independent Variable (input): The number you need to locate the function of; the x in f(x).
    • Dependent Variable (output): The outcome of replacing the independent value into the function, f(x). (This is like y variable.)
    • Domain: The set of all feasible values of the autonomous variable.
    • Range: The set of all feasible values of the dependent variable.

    Realm of function

    The realm of a function is the set of all the numbers that are feasible to be an input of a particular function, here the x in f(x). The domain can be thought of as the assortment of all the possible autonomous variable values that can be placed into a function.

    Only real numbers are incorporated in a domain. 

    Range of function

    This can be defined as the assortment of all the numbers that can certainly be the outcome of a function, for instance, the value for f(x). 

    GMAT Algebra: Inequalities

    Inequality can be defined as such as "x is less than y" or "x is greater than or equal to y". Adjoining all the common symbols that have been taught to us like addition, deduction, multiply and division, mathematics clubs certain symbols to present how the two sides of an equation are connected.

    Mathematical Symbols denoting Equality and Inequality

    Inequality is a statement that uses one of the following symbols:

    • = : equal to
    • ≠ : not equal to
    • ≅ : approximately equal to
    • > : greater than
    • ≥ : greater than or equal to
    • < : less than
    • ≤ : less than or equal to

    Mathematical operations with inequalities

    It is known that while dealing with a particular equation, the students solving GMAT algebra separates the variables on one side and implement similar operations on both sides. Here, one thing has to be noted, while doing this if the student comes across negative numbers they need to reverse the direction of the inequality sign.

    Like,  -2x ≤ 10 & x ≥ 5

    • Working with transitive numbers,
    • Transitive property,
    • Addition of like inequalities

    The GMAT algebra syllabus dwells sums which are tricky but can be solved after following proper preparation tips for GMAT. The GMAT algebra syllabus can be quite deceptive in a few parts. The students are always advised to minutely notice the question, only then they would be able to utilize the time without fretting. 

    *The article might have information for the previous academic years, which will be updated soon subject to the notification issued by the University/College

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