Key Differences Between Variables and Constants in Year 10 Mathematics

In algebra, it's important to know the difference between variables and constants. This understanding helps with working on algebraic expressions.

1. Definitions:

• Variable: A symbol, usually a letter like $x$, $y$, or $z$, that stands for a value that can change. For example, in the expression $3x + 2$, $x$ is a variable.
• Constant: A number that stays the same. In the expression $3x + 2$, the number 2 is a constant.

2. Characteristics:

• Values:

  • Variables can have many different values. For example, they can be any real number.
  • Constants have only one value that doesn’t change, like $\pi \approx 3.14$.

• Role in Expressions:

  • Variables often represent unknowns and are important for creating equations.
  • Constants give us specific numerical information.

3. Examples:

• Take the equation $2x + 5 = 13$. Here, $x$ is a variable that can change. When you replace it with the right number, the equation works. The number 5 is a constant.

4. Importance in Mathematical Operations:

• When you do calculations, knowing how to work with variables and constants is very important. You can change the values of variables to find answers, while constants always stay the same during calculations.

5. Use in Graphing:

• Variables usually help to define the axes on a graph. For example, in a Cartesian plane, $x$ is the variable along the horizontal axis. Constants can show fixed points, like $y = 0$, which represents the x-axis.

Knowing these key differences makes it easier to solve problems and improves your skills in algebra during Year 10.