Preparation for Algebra Aptitude Tests

The mere purpose of these aptitude testing is to measure your overall mathematical capability in general and your algebraic ability in particular. The questions are designed in a way to help the psychologists to find out what your achievements tests fail to exhibit. How efficiently you can 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 aptitude tests may include all these questions or any of them...

Algebraic Expressions and Algebra Aptitude Tests

The psychologists use a number of 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 trinomial, 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

An expression which cannot be written in the form of P/Q, where P and Q are polynomials and Q ≠ 0, 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

• 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

Formulae for Algebra Aptitude Tests

1- (a+b) = a+b+2ab

2- (a-b) = a+b-2ab

3- (a+b) + (a-b) = a(a+b)

4- (a+b) - (a-b) = 4ab

5- (a+b) = (a-b)  +4ab

6- (a-b)  = (a+b)  - 4ab

7- (a+b+c)  = a+b+c+2(ab+bc+ca)

8- 1/2[(a-b)  + (b-c)  + (c-a) ] = a+ b+c-ab-bc-ca

9- (a+b)(a-b) = a-b

10- (x+a)(x+b)=x+x(a+b)+ab

11- x(a+b) = ax + bx

12- a-b = (a+b)(a-b)

13- (a+b)=a+b+3ab(a+b)

14- (a-b)  = a-b-3ab(a-b)

15- a+b = (a+b)(a+b-ab)

16- a-b = (a-b) (a+b+ab)

17- a+b+c-3abc = (a+b+c) (a+b+c-ab-bc-ca)

18- (x+a)(x+b)(x+c) = x+x(ab+bc+ca) + x(a+b+c)+abc

You need to review these formulae before you encounter any numerical aptitude test because most of them include problems involving these formulae. However, a continuous practice shall make algebra aptitude tests easier.

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