Exam Questions - Substitution types

Exam Questions - Substitution types

Understanding Substitution Types

• Substitution in algebra is a technique used to alter an equation or inequality which makes it simpler to understand or easier to solve.

• It typically involves you taking a portion of a mathematical expression or equation and replacing it with an equivalent entity.

• The main types of substitution used in algebra include simple substitution, substitution in equations, substitution to remove roots and substitution in integration.

Simple Substitution

• Simple substitution process involves replacing one variable with another one.

• It is often used in instances where the solution to the problem becomes more straightforward after replacing variables.

Substitution in Equations

• Substitution in equations typically involves replacing one or more variables in an equation with others such that the equation remains balanced or equal.

• This type of substitution is prevalent in the solution of simultaneous equations.

Substitution to Remove Roots

• Substitution to remove roots involves replacing the radical part of an equation or expression with a new variable, mainly to remove the square / cube root or any other root.

• Post substituting, the equation becomes a polynomial equation, which is generally easier to solve.

Substitution in Integration

• Substitution in integration, often termed as the substitution rule, is a primary method in integral calculus.

• It involves changing the variable of integration (often denoted as x) to another variable, simplifying the integral and making it easier to solve.

Solving Exam-style Questions Using Substitution

• Practice is crucial to become efficient in using substitution in algebra effectively.

• Complete as many example problems as you can find, trying to identify what type of substitution would be best for each problem.

• Begin with the most straightforward problems and gradually work your way up to more complicated problems.

• Always ensure to check your answers after you’ve completed a problem to confirm whether you’re substituting correctly.

By practising the different types of substitutions regularly, you’ll familiarise yourself with identifying the right type of substitution to use and become quicker and more accurate in applying the method to solve algebraic problems eventually.