# MATH 1200- Final Exam Guide - Comprehensive Notes for the exam ( 72 pages long!)

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MATH 1200
FINAL EXAM
STUDY GUIDE
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Rectangular coordinate system
is formed by using real number lines intersecting at right angles
x-axis
the horizontal real number line
y-axis
the vertical real number line
origin
the point of intersection of the x- and y-axis
quadrants
the plane divided into four equal parts
ordered pair
the points of correspondence between real numbers on the x- and y-axes.
x-coordinates
the directed distance from the y-axis
y-coordinates
the directed distance from the x-axis
Pythagorean Theorem
a^2+b^2=c^2
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d= √((x_2-x_1)^2+(y_2 - y_1)^2 )
Midpoint formula
M=(((x_2+x_1))/2- ((y_2+ y_1))/2)
Equation in two variables
A relationship between two quantities
Solution or solution point
An ordered pair (a,b) is the solution of an equation if the equation is true
The graph of an equation
The set of all points that are solution of the equation
Sketching the graph of the equation by plotting points
1. If possible rewrite the equation so that one of the variables is isolated on one side of the
equation
2. Make a table of values showing several solution points
3. Plot these points on a rectangular coordinate system
4. Connect the points with a smooth curve or line
Finding the intercepts
1. To find the x-intercepts, let y be zero and solve the equation for x
2. To find the y-intercepts, let x be zero and solve the equation for y
Graphical Tests for Symmetry
1. A graph is symmetric with respect to the x-axis if, whenever (x,y) is on the graph, (x,-y) is
also on the graph
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