Algebra - Solving Equations

Question 1

What is a linear equation?

Answer 1

A linear equation is an equation where x to the power of 1 is the highest order term.

Question 2

What rules must we always follow when solving linear equations?

Answer 2

When solving linear equations, we must always follow the rule that whatever we do to one side we must do to the other.

Another rule we must follow is to always move the smallest values over.

Question 3

(Example of a linear equation)

Answer 3

4(2x+3)=5x-7

Question 4

What is a quadratic equation?

Answer 4

A quadratic equation is one in which the highest order x term is x squared.

Question 5

How do we solve a quadratic equation?

Answer 5

To solve a quadratic equation we factorise by using either product and sum or the quadratic formula.

Question 6

What do we need to make sure before solving a quadratic equation through factorising?

Answer 6

Before solving a quadratic equation through factorising, we need to make sure the equation is in the form:
ax2+bx+c=0

Question 7

What can we do to both sides of this equation which has been factorised using a common factor from 4x2-16=0: 4(x2-4)=0

Answer 7

We can divide both sides of the equation in the equation 4(x2-4)=0 by 4, because the equation is equal to 0.

Question 8

When should we use the quadratic formula?

Answer 8

We should use the quadratic formula if we cannot factorise our quadratic.

Question 9

What is the quadratic formula?

Answer 9

The quadratic formula is: x equals minus b plus or minus the square root of b squared minus 4ac all over 2a
For ax2+bx+c=0
(On the formula sheet)

Question 10

When solving a quadratic formula how should we do the calculation in our calculator?

Answer 10

When a solving a quadratic formula, in our calculator we should always work out the answer for the top line first and then divide.