# Preparation for Algebra Aptitude Tests

You can find questions categorized for algebra aptitude tests in any numerical aptitude test. However, you may encounter them separate as well for some particular job or training course. In either of the situations, such questions are going to make some impact upon your future career life.

The mere purpose of the mathematical aptitude tests is to measure your overall numerical capability. However, when you are offered specific algebra tests then focus of the examiner is on your algebra capabilities and skills.

The questions are designed in a way to help the psychologists to find out what your achievements tests fail to exhibit.

How efficiently can you learn algebra? How can you interpret algebraic expressions?

How can you choose an equation to solve short verbal problems?

Can you identify relationships in different sets of numbers?

How do you use algebraic symbols?

The algebra tests may include all these concepts and many others.

## Algebraic Expressions and Algebra Aptitude Tests

The psychologists use various algebraic expressions to design algebra aptitude tests. An expression which connects variables and constants by algebraic operations of addition, subtraction, multiplication, division and root extraction is called an algebraic expression. For example, 5x-3y and √a+1/√a are algebraic expressions.

There are three major types of algebraic expressions; polynomials, rational and irrational.

Polynomial Expressions

A polynomial is an algebraic expression consisting of one or more terms in each of which the exponent of the variable is zero or a positive integer. For example, 68 + x or x +15/3 are polynomial expressions with one variable while 7x + 5x or 6y – 3y are polynomial expressions with two variables.

The polynomials used in algebra aptitude tests are named as monomials, binomials, and tri-nomial, depending upon the number of variables used in the algebraic expressions.

Rational Expressions:

An algebraic expression in the form of P/Q, where P and Q are polynomials and Q is not equal to zero, is called a rational expression. For example the expression 2x + 6/ x where x ≠ 0, is a rational expression.

Irrational Expressions:

When you can't write an expression in the form of P/Q, where P and Q are polynomials and Q ≠ 0, it is called an irrational expression. The expressions which involve square root of the polynomials are included in this category of the polynomials.

## Algebra Aptitude Test Problems The algebra aptitude tests offer various algebraic problems to be solved. Some of the basic problems include:

•    Evaluation of an expression

•    Addition and subtraction of monomials

•    Addition and subtraction of polynomials

•    Multiplication of monomials

•    Multiplication of binomials

•    Multiplication of trinomials

•    Factoring out a common divisor

•    Factoring the difference of squares

•    Factoring the squares of binomials

•    Greatest Common Divisor (G.C.D)

•    Least Common Divisor (L.C.D)

•    Simplification of an algebraic fraction

•    Square root of an algebraic expression

•    Exponents

## Formula for Algebra Aptitude Tests

You can prepare algebra aptitude tests by learning some basic algebraic formulas.

• a⁄b + c⁄d = (ad + bc) ⁄bd
• a⁄b - c⁄d = (ad - bc) ⁄bd
• a⁄b x c⁄d = (a x c) ⁄(b x d)
• a⁄b / c⁄d = (a x d) ⁄(b x c)
• (a + b)² = a² + 2 ab + b²
• (a - b)² = a² - 2 ab + b²
• (a + b)²- (a - b)²=4ab
• a² - b² = (a + b) (a - b)
• a² + b² = (a + b)² - 2ab
• a² + b² = (a - b)² + 2ab
• a² + b² = ½ [(a + b)² - (a - b)²]
• ab = ¼ [(a + b)² - (a - b)²]
• (a - b)² = (a + b)² - 4 ab
• (a + b)² = (a - b)² + 4 ab
• (a+b+c)² =a²+b²+c²+2ab+2bc+2ca
• (a-b+c)² =a²+b²+c²-2ab-2bc+2ca
• (a-b-c)² =a²+b²+c²-2ab+2bc-2ca
• (a + b)³ = a³ + 3 a² b  + 3 a b² + b³
• (a - b)³ = a³ - 3 a² b  + 3 a b² - b³
• a³ + b³ = (a + b)³ - 3 ab (a + b)
• a³ + b³ = (a + b)³ - 3 ab (a + b)
• a³ - b³ = (a - b)³ + 3 ab (a - b)
• a³ - b³ = (a - b) (a² + ab + b²)
• a³ + b³ = (a + b) (a² - ab + b²)

You need to review these formulae before you encounter any numerical aptitude test because most of them include problems involving these formulae. But this is not an exhaustive list. You can find many such formulas on internet. A valuable free source of algebra formulas is here.

The key of success is simple; practice, practice and practice.

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