Constants – Fixed Values in Algebra
A constant is a value that does not change. In algebra, constants appear alongside variables in expressions and equations. Recognising them helps you understand the structure of any algebraic statement.
What Is a Constant?
A constant is a fixed number whose value never changes within a given problem. It may be a plain number like 5, or a named constant like pi (approximately 3.14159).
Constants vs Variables
| Constant | Variable | |
|---|---|---|
| Value | Fixed | Can change or is unknown |
| Example in 3x + 7 | 3 and 7 | x |
| Written as | Plain numbers or named symbols | Letters (x, y, n, etc.) |
Famous Mathematical Constants
| Constant | Symbol | Approximate Value | Where Used |
|---|---|---|---|
| Pi | pi | 3.14159... | Circle circumference and area |
| Euler number | e | 2.71828... | Exponential growth and logarithms |
| Golden ratio | phi | 1.61803... | Art, nature, and geometry |
Constants in Expressions
In the expression 5x + 3, the number 5 is a coefficient (a constant multiplied by a variable) and 3 is a standalone constant called a constant term. Both are fixed numbers — they do not depend on x.
4 is the coefficient of t squared. 7 is the coefficient of t. 12 is the constant term. The variable is t.
pi is a constant (approximately 3.14159). r is a variable (the radius can be any value). A is also a variable (it changes as r changes).
Why Constants Matter
Constants set the scale and shift of algebraic relationships. In y = 2x + 3, the constant 2 controls how steeply y grows with x, and 3 shifts the whole relationship up by three units. Changing a constant changes the entire behaviour of the expression.
Key Takeaways
- A constant is a fixed number that does not change in a given context.
- Coefficients are constants multiplied by variables.
- Constant terms stand alone — they are not multiplied by any variable.
- Famous constants like pi and e appear throughout mathematics and science.
Practice Questions
- In 6m - 9, identify the coefficient and the constant term.
- In the formula C = 2 pi r, which symbol is a constant and which is a variable?
- If the expression 3x + k equals 11 when x = 2, find k.
- Write an expression with one variable, one coefficient, and one constant term.
- In y = 4x + 7, what does changing the constant 7 do to the graph?