CMIS 102A

Math stuff needed for the course.

4 arithmetic operators: + - * /
they must be used, there's no "4a" meaning "4 times a" like in algebra.
4*a the operator must be written.
4/a is "4 divided by a"
The normal algebraic order of operations applies in Java.  Parentheses
override the normal order.
In Java, if a number does not have a decimal point it is an
integer. Division of integers is whole number division and there is no
decimal point in the result:  7/2 is 3 (not 3.5)  
Integer division by zero isn't allowed.

Evaluate these Java arithmetic expressions: (i.e. what's the answer)
7+5*3
7+5/3
7-5-3
7*5/3
7+5*3-2
7+5/3-2
7*5-3*2
7/5-3/2
7*5*3*2
7/5*3/2
7/5/3/2
7-5-3-2
(7+5)*3
7+(5*3)
7-(5-3)
(7+5)*(3-2)
7+5*(3-2)
7+(5*(3-2))

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Pythagorean theorem:
in a right triangle (one with a 90 degree angle), the length of the
hypotenuse (the side opposite the right angle, and the longest side)
is equal to the square root of the sum of the squares of the other two
sides. 
What is the hypotenuse of the right triangles with the following side
lengths?
3 and 4

6 and 8

3 and 3

1 and 1


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Circles:  
diameter is twice the radius (radius is half the diameter).
PI is approximately 3.14159... (it's the ratio of the circumference to
the diameter)
circumference is 2 times the radius times PI
area is radius squared times PI

What are the circumference and area of these circles:

radius 1

radius 2

diameter 20



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In a Cartesian x,y coordinate system (think graphing of functions etc)
each point has an (x,y) coordinate.  
What are the four corner coordinates of a rectangle that is 200 wide and 300
tall whose lower left coordinate is at (0,0)?  What is the coordinate
of the center of the rectangle?  What are the four corner coordinates of
the rectangle that is half the size that is centered on the same
center point as the outer rectangle?


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Java has a fifth arithmetic operator: % which is the "mod" (short for
modulus) operator.  It's a remainder operator, the remainder after
dividing: 7%2 equals 1, the remainder after dividing 7 by 2 (think
about when you first learned division, "2 goes into 7 three whole times,
with a remainder of 1").  This % operator has nothing to do with
percent; some punctuation symbol was needed, and % does have a / in
it, sort of like division.  Mod by 0 isn't allowed.
Evaluate:
5%5
5%4
5%3
5%2
5%1
5%0
5%6

To get the number of whole minutes in a large number of seconds,
integer divide the seconds by 60 and mod it by 60 to get the remainder
seconds. 
320 seconds is how many minutes and seconds?