GRE Algebra

Wondering what Algebra questions are asked in the GRE exam? Through the course of this article, we will acquaint you with the GRE Algebra syllabus, some basic concepts and formulas, question types and more. But, before we begin, we will give a brief explanation of the GRE quantitative section. 

GRE Quantitative Section 

The GRE quantitative section tests you on various mathematics concepts such as data analysis, arithmetic, geometry and algebra. There are about 40 questions in this section. The GRE quantitative section is scored between 130 to 170, these scores increase by a one-point increment. Since the GRE is a computer-adaptive test, the score of each question is calculated with regards to its difficulty level.

The GRE quantitative reasoning has about two kinds of multiple-choice questions, a numeric entry question, and a quantitative comparison question. All in all, there are four types of questions which we will explain in the following section.

GRE Quantitative Question Types 

The GRE quantitative question types are as follows: 

• Multiple-choice – Select one choice: These questions require you to select one choice amongst the five choices given to you.

• Multiple-choice – Select one or more answers: These questions require you to pick one or more appropriate answers from the given set of choices. However, the question does not indicate if you are to choose one or more answers, you have to use your own discretion and choose the right answers.

• Quantitative comparison: Quantitative comparison questions require you to compare two different kinds of quantities and pick a corresponding statement, which describes the comparison accurately.

• Numeric entry: These questions require you to solve a word problem and enter the values of the answer into a designated box. If the answer is a fraction, then two boxes will be provided to you, one for the denominator and one for the numerator. 

Algebraic questions can be asked in any question format, but the most common format is the multiple-choice questions. 

GRE Algebra Syllabus 

The topics of the GRE algebra syllabus are as follows:

• Basic equations 
• Equations with square roots 
• Quadratic equations
• Equations with fractions 
• Graphs of quadratics 
• Coordinate plane
• Equations of lines
• Equations involving exponent 
• Equations with absolute values
• Systems of equations 
• Three types of factorisation 
•  Simplification of algebraic expressions 
• Expanding expressions  

While these topics seem complex, it is much easier to comprehend them if you are thorough with the fundamental concepts of algebra. 

GRE Algebra Concepts

There are usually six algebra questions in the GRE quantitative section. These questions are based on some fundamental concepts. In order to ace the section, you need to be familiar with GRE algebra concepts that are as follows: 

1. Constant: The value of constant doesn’t change no matter what. For example, x + 9, the constant is 9.   
2. Variable: When the value is unknown, an alphabet is used to denote that specific value. Some of the commonly used alphabets are a, b, c, d, x, y.
3. Term: A term often refers to a constant or the product of the constant. It also contains one or more variables. For example, 5ab, 4x.
4. Algebraic Expression: An algebraic expression is a combination of two or more terms. These terms are often connected with addition, subtraction, and division symbols. For example, x² + x – 2, 3ab , 6ab + 9cd.
5. Monomial: A monomial refers to a single term such as 5x. 
6. Polynomial: It is a general term for an algebraic expression that contains one or more terms.
7. Trinomial: A trinomial refers to an algebraic expression with three terms.
8. Binomial: A binomial refers to an algebraic expression with two terms. 

Below we have mentioned some GRE algebra formulas that you need to practise to prepare for the GRE exam. 

GRE Algebra Formulas 

Linear and Quadratic Inequalities 

Inequalities in algebra occur if you are dealing with comparisons. It will contain inequality symbols such as ＜,≤,≥,＞. Linear inequalities is when the expression contains a linear function. Quadratic inequalities, on the other hand, are inequalities that contain a quadratic expression in them. 

Exponents and Radicals 

You need to remember these formulas when dealing with exponents and radicals:

• xa/xb= xa-b
• (xa)b= xab
• xaxb= xa+b

Substitution and Elimination Methods 

Substitution method is one of the common ways to solve algebra equations. When there are two equations provided with variables and values, you can substitute the values in the next equation and decipher the unknown values.

GRE Algebra Practise Questions

The GRE algebra practise questions will help you understand the format of the questions and how each question is solved. Here are some practice questions from ETS  official site as follows: 

1. y= 2x² + 7x -3

Quantity A =  x 

Quantity B =  y

1. Quantity A is greater.
2. Quantity B is greater.
3. The two quantities are equal.
4. The relationship cannot be determined from the information given.

Explanation: If x= 0, then y= 2(0²) + 7(0) -3 = -3. So, in this case x＞y; but if x=1, then y = 2(1²) + 7(1) – 3 = 6. So, in that case, y ＞x. Thus, the correct answer is Choice D, the relationship cannot be determined from the information given.

b)  If 5x + 32 = 4 – 2x, then what is the value of x ?

1. -4
2. -3
3.  4
4.  7
5. 12

Explanation: If you solve the equation for x, you get 7x = -28. So, x = -4. Hence, the correct answer is Choice A, -4.

We have provided an in-depth guide to the GRE Algebra, which includes the formulas to be used, concepts to be learned, the question formats and have even provided a sample question Now, all there is left for you to do is prepare and perform outstandingly well in the GRE.