Topic outline
- Introduction
- Informations and news
Informations and news
The aim of the course is to introduce the student to the concept of equation, to their distinction, to the focus on the concept of the first degree equation and its connection with the linear type function.
- The Equations
The Equations
"Regarding the resolution of a problem related to numbers o to the abstract relations between quantity, it is only necessary translate the problem from just language to language algebra ". Isaac Newton
Intro to equations
Learn what an equation is and what it means to find the solution of an equation.
PRE-REQUISITI
- Breakdown of polynomials into factors
- Algebraic calculus with monomials, polynomials
- Algebraic fractions
- Notable products
We call equation the equality between two algebraic expressions, functions of the same variables, which is verified only for values that are attributed to these variables. The expression on the left of the equality symbol is called the first member, the one on the right is called the second member. The variables of the two expressions are called in unknown.
What is an Equation
An equation says that two things are equal.
It will have an equals sign "=" like this:
7 + 2 = 10 − 1
That equation says: what is on the left (7 + 2) is equal to what is on the right (10 − 1)
So an equation is like a statement "this equals that"
Here is another equation:
Parts of an Equation
So people can talk about equations, there are names for different parts (better than saying "that thingy there"!)
Here we have an equation that says 4x − 7 equals 5, and all its parts:
A Variable is a symbol for a number we don't know yet. It is usually a letter like x or y.
A number on its own is called a Constant.
A Coefficient is a number used to multiply a variable (4x means 4 times x, so 4 is a coefficient)
Variables on their own (without a number next to them) actually have a coefficient of 1 (x is really 1x)
Sometimes a coefficient is a letter like a or b instead of a number:
Example: ax2 + bx + c
- x is a variable
- a and b are coefficients
- c is a constant
An Operator is a symbol (such as +, ×, etc) that shows an operation (ie we want to do something with the values).
A Term is either a single number or a variable, or numbers and variables multiplied together.
An Expression is a group of terms (the terms are separated by + or − signs)
So, now we can say things like "that expression has only two terms", or "the second term is a constant", or even "are you sure the coefficient is really 4?"
AIMS
Knowledge:
Acquire the concepts of identity and equation · Know the principles of equivalence · Knowing how to recognize certain, indeterminate and impossible equation
Skills
♦ Recognize identities and equations ♦ Knowing how to apply the principles of equivalence to solve the equation ♦ Solve and verify a first degree equation ♦ Knowing how to solve problems with equations and being able to evaluate if the solution obtained is acceptable
- Two variable linear equations and their graphs
