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

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NSU

MATH 1200

FINAL EXAM

STUDY GUIDE

SET 1

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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Distance Formula

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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