The topic Algebra follows directly from the topic Number as we start to do arithmetic operations with letters instead of numbers.
The letters are used to represent unknown values. Being able to do calculations with values that we don’t know makes mathematics much more powerful, as we can find more general solutions that can then apply for a variety of input values.
We start below by looking at algebraic expression, which are ways of stating something using algebra. Being confident ad changing the form of these will be very valuable to us through our Algebra course:
- Simplifying Expressions;
- Expanding Brackets;
- Introducing Functions;
- Expressions to Represent Word Problems.
Now that we are more familiar with algebraic expressions, we can combine more than one expression into a relationship known as an equation. Solving these equations is possibly the most important task that algebraists face. We will also briefly introduce formulae:
- Solving Equations – Function Machine;
- Solving Equations – Balancing;
- Equations to solve problems;
- Substituting into expressions and using formulae.
Arguably the biggest breakthrough in the history of mathematics was at the beginning of the 17th century, when the great Enlightenment thinker René Descartes introduced a new system that linked our knowledge of geometry (inherited primarily from Greek culture) with our knowledge of algebra (inherited primarily from Arab culture). We call this system Cartesian Geometry or Coordinate Geometry.
Let’s practice the work we’ve done above on coordinate geometry before moving on to the next section.
We end this year’s work on algebra by looking more closely at sequences and functions and the associated concept of linear graphs.
Before we test ourselves on this material, let’s practice it a little here.