GRE Algebra Syllabus, Question Types, and Practice Papers

GRE algebra tests candidate’s basic algebra skills and concepts from high school or middle school. About 25 percent of the GRE questions in the test are in elementary algebra, linear algebra, abstract algebra, and number theory. Out of 20 questions, the GRE algebra questions have a weightage of 6 questions. The concept of algebra questions may appear in 4 different types namely- problem-solving, quantitative comparison, numeric entry, or more than one correct answer. Solving GRE algebra practice questions regularly will help candidates to get familiar with the GRE algebra question types, algebraic terminology, and the instructions provided with the questions.

GRE Algebra Concepts

The algebra GRE questions are related to reasoning, problem-solving, data interpretation, and more. Here are a few algebraic terms that form an integral part of the GRE algebra concepts.

• Variable: A letter is used to present a quantity whose value is unknown. For instance, x, y, a, b, c, and d are commonly used variables.
• Term: A term is referred to as a numerical constant or the product (or quotient) of a numerical constant and one or more variables. For instance, 3x, 5x2
• Algebraic expression: It is a combo of one or more terms with each term connected with the addition or subtraction symbols. Like, as 3xy, 4ab − 5cd, and x²+ x − 1.
• Coefficient: If we consider the previous point’s example, in the term 3xy, 3 is the coefficient.
• Constant: Like its literal meaning, it means the value which doesn’t change. Like in x + 6, 6 is a constant.
• Monomial: It is a singular algebraic term like -5x or 3a2
• Polynomial: It is the regular name for algebraic expressions with more than one term
• Binomial: A polynomial with two terms
• Trinomial: A polynomial with three terms

GRE Algebraic Expressions 

An algebraic expression comprises one or more variables. It can be written as a single term or as a sum of terms.

Here are four examples of algebraic expressions.

Example 1: 2x

Example 2: y -1/4

Example 3: w3z+5z2-z2+6

Example 4: 

The following are three basic types of equations.

Type 1: A linear equation in one variable:

for example: 3x +5 =-2

Type 2: A linear equation in two variables:

for example: x - 3y = 10

Type 3: A quadratic equation in one variable:

for example: 20y2 + 6y -17=0

GRE Algebra Basic Equations

To solve these basic equation problems, candidates need to make a table from the given question and draw the equation from it to solve the question.

Example:

In a research and development department, 14 workers have a PhD, and 30 workers don't have a PhD degree. In the department, the number of women that do not have a PhD degree is 10 greater than the number of women who do have a PhD. If a third of the men working in the department have a PhD degree, then how many women work in the department?

A) 16
B) 18
C) 26
D) 28
E) 32

This is a set problem and a table will make things easier.

Let x = the number of women who have a PhD.

Let y = the total number of men who work in the department.

The table thus becomes:

The box marked with the question mark is the one we want to fill in with our answer. The table is an additional table, so you can add horizontally and vertically. Set up two simultaneous equations:

1) x + x + 10 = 44 – y
→ 2x + 10 = 44 – y
→ 2x + y = 34

2) x + y/3 = 14
→ 3x + y = 42
Solving these equations would give the answer to the question.

GRE Algebra Rules of Exponents and Radicals

There are three basic rules of exponents:

• xaxb=xa+b
• xa/xb=xa-b
• (xa)b=xab

Together with the rule for converting radicals into exponents, every other property basically derives from these rules.

Example: q√xp = xp/q

Example: If where and are integers, what is in terms of ?

(A)

(B)

(C)

(D)

(E)

GRE Algebra Solving Equations in One Variable

On the GRE, you may need to solve for an unknown in an equation with multiple variables.

Example: Solve  for  in terms of .

(A)

(B)

(C)

(D)

(E)

GRE Algebra Linear/Quadratic Inequalities

Inequalities GRE questions are one of the GRE algebra concepts which state relationships of comparison. You will get to know if you are dealing with inequality if you find these symbols: < > ≤ ≥.
GRE math inequalities are a distinctive type of linear variety. If a quadratic or another kind of expression shows up, then the analysis becomes trickier.

Example:

GRE Algebra Simultaneous Equations in Two Variables

This is another common sum in the GRE algebra practice. There can be sums with multiple variables for which substitution or elimination methods are required.

Example: 

GRE Algebra GRE Word Problems

GRE algebra word problems have different methods of solving. Each word problem requires a different algebra GRE strategy guide instead of only finding a solution to the problem.

Example: Terry wants to invest . What annual simple interest rate would be required in order for Terry to have a balance of   by the end of three years?

Tip: To solve the above problem, try using the simple interest formula for the unknown rate.

GRE Algebra Functions and Their Graphs

Functions are the rules that state numbers to solve an equation. For instance, the function states to input different variables.

Example: If the graph of the function  goes through the point  , what is the value of ?

(A) 4
(B) 6
(C) 7 
(D) 8
(E) 10

GRE Algebra Coordinate Geometry

In coordinate geometry, two real number lines when perpendicular to each other, intersect at zero points explaining a rectangular coordinate system. This is also called the xy-coordinate system or xy plane.

For instance, to know the slope-intercept form for lines (y=mx+b).

Example: What is the -coordinate where the line through (13,-7) and (-7,5) crosses the -axis?

GRE Algebra Symbolism

One very important feature seen in the GRE quant section is different kinds of symbols like ★, ✧, and ♦. Don’t stress seeing this as these kinds of problems will just require a substitution method. Reading the question carefully, understand what the symbol stands for, and accordingly answer. GRE algebra practice questions help you to get familiar with such concepts.

Example: If x ★ y = 2x2 − 3y, what is the value of 4 ★ 8?

1. 2
2. 4
3. 8
4. 12
5. 16

GRE Algebra Sequences

Sequences are a list of numbers and the value of a number in a sequence is recognized by its position. It is generally presented as:

s s₂, s₃,…sn,…

Example: A sequence is defined by the following formula:

S1 =12

What is the 4th element of this sequence?

Possible Answers:

1. 41
2. 1172
3. 389
4. 29
5. 145