Star-ED
Formerly Star Tutorials
Tutoring in Math Physic(Mechanics), Electronics & Computer Software.
"Algebra"
"Trig"
"Equations"
For help contact me via e-mail and I will put a similar
problem on the web with the steps for the solution.
Equation Manipulation:
Take the simple equation:
4x = 24
Ask the following questions.
What am I looking for?
I am looking for "x"
What is happening to it?
It is being multiplied by 4
What is the opposite action?
Dividing by 4
Actions done to on side of the equation must be done exactly on the other side
in order to preserve equality.
4x/4 = 24/4
On the left side of the equation the 4's cancel and on the right side 24/4 = 6 therefore:
x = 6
These steps can be taken with any equation regardless of complexity.
Example 2:
12xy = 20k6j: solve for "x"
Step #1: divide both sides by 12y
x = 20k6j/12y
The fact that we do not have a numerical value for x is immaterial.
Our objective was to solve for "x" which means isolating it on one side of
the equation. End of story! Do not make it more difficult than it really is!
Here's what happens when ther is a fractional equation.
3x/5 = 2y
Multiply both sides of the equation by 5
5*3x/5 = 5*2y
The 5's cancel on the LHS and on the RHS 5*2y = 10y
3x = 10y
Divide both sides by 3
3x/3 = 10y/3
The 3's cancel on the LHS
Answer: x = 10y/3
If you would like more samples please click on "Contact" and send me a problem.
The following is the solution to a problem found in most math books to encourage logical thinking.
Problem:
A car passes a store at a speed of 50 km per hour. Five minuts later a second car passes the store
at a speed of 80 km per hr. How far past the store will the second car overtake the first car?
Solution:
D2 = 80 *(50*(5/60))/(80-50) (recall 5 min is 5/60 hours)
D2 = 11.11 km
Try this formula with various speeds.
Basic Geometry
The following notes are Geometry concepts that you may find very useful in the study of Algebra.
Angle:
The figure formed by two straight lines with a common origin and different terminal points is called and angle.
Vertical Angles:
Two angles that have a common vertex and the sides of one prolongations of the other. Or two straight lines
that cross each other will create vertical angles.
Adjacent Angles:
Two angles that share the same vertex and have a common side between them.
Perpendicular Lines:
Two lines are perpendicular if the meet so as to form two equal adjacent angles.
These angles will be 90 degrees each.
Parallel Lines:
Two or more lines in the same plane are parallel if they are perpendicular to the same line.
Right-angle:
If the sides of an angle are perpendicular to each other the angle is a right-angle
Straight-angle
A straight angle is equal to two right-angles. It may also be referred
to as a half of a revolution.
Acute Angle
Any angle less than a right-angle
Obtuse Angle
Any angle greater than a right angle but less than a straight angle
Complementary Angles
Any two angles whose sum is a right angle. Complementary angles do not
necessarily have to be adjacent.
Supplementary Angles:
Two angles whose sum is a straight line (1800). It is not necessary for
supplementary angles to be adjacent.
Triangles
A tri-angle is a plane figure made up of three line segments that meet a
three distinct points.
Equilateral tri-angle:
A tri-angle with equal sides, An equilateral tri-angle also has equal angles.
Isosceles triangle:
A triangle with two equal sides
Right triangle:
A triangle that contains a right-angle
Obtuse triangle:
A triangle that contains an obtuse angle (<90<180)
Acute triangle:
A triangle with all angles acute. (>90)
Theorems:
§87: If two parallel lines are cut by a transversal the interior angles on the
same side of the transversal are supplementary.
§175: The bisectors of the angles of a triangle are concurrent.
(they bisect each other equal-distance from each side)
Algebra -
Trig -
Equations -