We can also sum up a series, where Sigma Notation is very useful. Systems of Linear and Quadratic EquationsĪ Sequence is a set of things (usually numbers) that are in order.Solving Systems of Linear Equations Using Matrices.Using Elementary Row Operations (Gauss-Jordan).What happens when we have two or more linear equations that work together? They can often be solved! It isn't very hard but can take a lot of calculations. We learned about inequalities above, now let's learn how to solve them. Mathematical Models and Mathematical Models 2.We already have experience in solving, but now we can learn more! It is the next major step after linear equations (where the exponent is 1, like x). "Second degree" just means the variable has an exponent of 2, like x 2. But from that simple foundation many useful things can be built.
But they come in many forms.Ī function relates an input to an output. But we need to be careful, as they sometimes don't give the full story. Graphs can save us! They are a great way to see what is going on and can help us solve many things.
They are simple, yet powerful in their ability to model real world situations. Polynomials were some of the first things ever studied in Algebra. We will be using exponents a lot, so let's get to know them well. Maybe we only know that something is less than, or greater than. "Equal To" is nice but not always available. Now we know what a set is, let us look at different sets of numbers that are useful: Next, we need to think about mathematics in terms of sets. So what is this thing called Mathematics? And how do you go about learning it? And don't guess the answer: use pen and paper and try your best before seeing the solution.
Answering questions helps you sort things out in your mind. do these! You need to balance your reading with doing. Near the end of most pages is a "Your Turn" section. With your new skills you will be able to put together mathematical models so you can find good quality solutions to many tricky real world situations. You will also gain a deeper insight into Mathematics, get to practice using your new skills with lots of examples and questions, and generally improve your mind.
You will learn about Numbers, Polynomials, Inequalities, Sequences and Sums, many types of Functions, and how to solve them.
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