Exercises
Numbers and relations
The set of Natural numbers is \( 1, 2, 3, ... 11, 12, 13 ...\)
The set of Whole numbers is \( 0, 1, 2, ... 11, 12, 13 ...\)
The set of Integers is \( ..., -3, -2, -1, 0, 1, 2, 3, ... \)
The set of Rational numbers is the set containg \( \frac{a}{b} \) where \( a \) and \( b \) are integers and \( b \neq 0 \)
The set of Irrational numbers is the set containg all numbers whose decimal part does not terminate or repeat and there is no imaginary i in the number.
The set of Real numbers is the set containing all rational and irrational numbers.
Properties of Addition
The property of closure is such that ...
Properties of Multiplication
Linear and Polynomials functions
The slope of a line is defined as \(m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \)
The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
The standard form of a linear equation is \( Dx + Ey = G \) where \( D, E, \) and \( G \) are all real numbers and \( D \) and \( E \) are not both 0.
The point-slope form of a linear equation is \( y - y_1 = m(x - x_1) \) where \( (x_1, y_1) \) is a point on the graph and \( m \) is the slope.
If two lines are parallel, then they have the same slope.
If two lines are perpendicular, then their slopes are the negative reciprocals of each other. For example, if the slope of one is \( \frac{a}{b} \), then the slope of the other is \( - \frac{b}{a} \).
Direct variation equation
A direct-variation equation is of the form \( y = c x \) where \( c \) is non-zero. \( c \) is called the constant of variation.
Proportion property in direct variation
For \( x_1 \neq 0 \) and \( x_2 \neq 0 \) and \( y = c x \) \( \frac{y_1}{x_1} = c = \frac{y_2}{x_2} \).