Algebra is an important branch of mathematics that involves using letters, numbers, and symbols to represent and manipulate mathematical expressions and equations. In GCSE Mathematics, algebraic concepts and techniques play a major role in solving various problems.
Let's start by considering a simple example:
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Suppose you want to find the value of a number 5 more than twice another number.
Let's call the unknown number "x" and the other number "y". Using algebra, we can write this as:
x = 2y + 5
Here, the letter "x" represents the number we want to find, "y" represents the other number, and the expression "2y + 5" represents the condition that the first number is 5, more than twice the second number.
Once we have set up the equation, we can use algebraic techniques to solve for "x". For example, we can rearrange the equation to get "y" in terms of "x":
y = \(\frac{(x-5)}{2}\)
Now, we can substitute any value of "x" into this expression to find the corresponding value of "y".
Another important concept in algebra is factorisation. This involves breaking down a mathematical expression into simpler terms that can be more easily manipulated or solved. For example, consider the quadratic equation:
x2 + 5x + 6 = 0
We can factorise this equation as:
(x + 2)(x + 3) = 0
This tells us that the solutions to the equation are x = -2 and x = -3.
Algebraic fractions can also be challenging for some students. However, with practice, they can become easier to handle. For example, consider the fraction:
\(\frac{(2x + 3)}{(x - 4)}\)
We can simplify this fraction by factorising the numerator:
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\(\frac{(2x + 3)}{(x - 4)}\) = \(\frac{(2x + 3)}{(x - 1)-3}\)
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= \(\frac{(2x + 3)}{(x - 1)-3}\) - \(\frac{(2x + 3)}{3}\)
