1.1 Simplify Expressions
Examples :
2(5x+6)-3x
2x²+x(4x+5)
x(4-x)-x(3-x)

1.2 Exponents and Radicals
Exponents : a^p
x⁰=1
x¹=x

y^a ×y^b =y^{a+ b}

\(\frac{x^a}{x^b}\) = \({x^{a-b}}\)

\((x^a)^b{}\) =  \(x^{ab}\)

\(x^{-a}\)  =  \(\frac{1}{x^a}\)

\((x* y)^a\)  =  \((x^a * y^a\)

|\((x^2 \)| = | \(|x|^2 \)| =   \(x^2 \)

  Radicals : \(\sqrt[n]{x}\)

\(\sqrt{x}\) =  \(x^{\frac{1}{2}}\)

\(\sqrt{x} × \sqrt{y}\) =  \(\sqrt{xy}\)

\(\sqrt{x} + \sqrt{y}\)  ≠  \(\sqrt{x} + \sqrt{y}\)

\(\sqrt{\frac{x}{y}}\)   =  \(\frac{\sqrt{x}}{\sqrt{y}}\) for  y  ≠   0

\(a\sqrt{x}± b\sqrt{x}\)   =  (a ± b)\(\sqrt{x}\)

\(a\sqrt{x}\)   =  \(\sqrt{a^2 × x}\)

Graph of y=\(\sqrt{x}\)

Question : Calculate \(\frac{6 + 3\sqrt{a}}{b}\)  when a=3 and b=9 ?

Simplify :  \(\frac{3^{4.5}x  2^{2.5}}{6^{2.5}}\) ?

1.3 Factoring Skills

(a + b)³  =  a³ + 3a²b + 3ab² + b³
(a – b)³  =   a³  – 3a²b + 3ab² – b³ 
a² – b²  =   (a + b)(a – b)
a³  – b³  = (a – b)(a² + ab + b²)
a³  + b³ =(a + b)(a² – ab + b²)

1.4 Linear Relations

A linear relation between 2 variables x and y can be written in the form
y=ax + b where a,b ∈R

This can also be written as
Ax + By=C where A,B,C ∈R and A≠0 ; B≠0

All linear functions can be graphed, y=f(x) is a staight line.
Graph of y=x+2

1.5 Quadratic Relations
A quadratic relation is of the form y=ax²+bx+c which represents a parabola. a,b ,c ∈R and a ≠0. If a=1, then y=x²+bx+c which can be factored as y=(x-p)(x-q)
Graph of y=x²+2x-1

1.6 Interval Notation
The interval notation is a way of writing subsets of the real number line. For example , {x | -2 ≤ x ≤3} can be written as, x ∈[-2,3]

1.7 Inequalities
1. Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own.
2. But these things will change direction of the inequality:
3. Multiplying or dividing both sides by a negative number
4. Swapping left and right hand sides
5. Don’t multiply or divide by a (unless you know it is always positive or always negative) variable

1.8 Test
Add mat

2. Functions and Characteristics
2.1 Functions and Relations

1^st Example :
f∶ R→ R

x↦ f(x)  =  \(\frac{x}{3x - 2}\)

f(x) exists only if x-2 ≠ 0 that is x≠2
The Domain of Definition is
D_f(x)=R- {2} = (-∞,2) ∪(2,+∞)
2^nd Example :
g∶ R→ R

x↦ g(x)=√(3-2x)

g(x)  exists only  if  3 – 2x ≥ 0 that is 3 ≥ 2x

x≤ \(\frac{3}{2}\)

The Domain of Definition is
D_(g(x))= (-∞,├ 3/2]