Number, Percent and Geometry Problems
Number Problems
To solve a word problem, it is helpful to remember some basic vocabulary:
Symbol Terms
sum
+
more than
Examples
The sum of two numbers is
five more than one number
difference
the length and the width d
Scientific Notation
Examples of Large and Small Numbers Using Scientific Notation
Example
Einstein's famous equation says that
E = mc2
where c is the speed of light
c = 300,000,000 m/sec
How much energy is emitted if 2,000 kg of matter is destroyed?
Solut
Relations, Functions, and Function Notation
Definition of a Relation, Domain, and Range
Examples
A.
Consider the relation that sends a student to that student's age.
B.
Consider the relation that sends a student to the courses that student is taking.
C.
C
Graphing Inequalities
Definition of a Linear Inequality
Definition
A linear inequality is an inequality that has one of the four forms below
1.
Ax + By < C
2.
Ax + By > C
3.
Ax + By < C
4.
Ax + By > C
We follow the follow the procedure listed below to gra
Operations on Real Numbers
Double Negative Signs
A negative of a negative is a positive, for example
(7) = 7
and in general
(x) = x
Addition Involving Positive and Negative Numbers
To add two negative numbers add then without the negatives and placing
Linear Equations and Word Problems
Algebraic Expressions
We will define the term variable which is analogous to a pronoun in grammar.
Definition
A variable is a symbol that represents a number that
may change depending on the circumstance.
Examples
We oft
Money, Mixture, Motion, and
Inequalities
Money Problems
Example
You have 40 coins in nickels and dimes. How many dimes do you have if you have a
total of $2.85?
Solution:
Our answer is
"We have _ dimes"
Let
d = the number of dimes you have
then
40  d = t
Slope
Lines and Slope
Definition
Let (x1,y1) and (x2,y2) be two points then the slope for
those two points is rise/run or
y2  y1
m=
x2  x1
Example:
For the points (1,2) and (5,3) we have
3  2
m =
5
=
51
4
Definition
A line through a point P with slo
Coordinates and Graphs of Lines
Solutions to Equations in Two Variables
Example
Consider the equation
2x + y = 10
We see that when
x=3
and
y=4
we have
2(3) + 4 = 10
is true. We say that (3,4) is a solution to the equation. We call (3,4) and ordered pair.
Set Definitions
The idea of a set is on of the fundamental concepts of mathematics. Below, we stat
the difinition.
Definition
A set is a well defined collection of objects.
Notation:
A = cfw_2,7,1
B = cfw_cat, dog, mouse
D = cfw_1,3,5,7,9,.
C = cfw_2,4,6,
Division of Polynomials
Dividing by a Monomial
To divide a polynomial by a monomial, we can divide each term by the monomial.
Example
4x2  2x  3
4x2
 2x
=

5x
5x
4x
=
2

5
3

5x
5x
3

5
5x
Exercises
Divide the polynomials
2x3 + 5x2  4
A.
3x
4
7x 
Exponentials and Order of Operations
Definition of an Exponential
Examples
32 = (3)(3),
43 = (4)(4)(4)
Definition of an Exponential
xn = (x)(x)(x)(x)(x).(x)
where there are n x's. x is called the base and n is
called the exponent
In the first example abov
Equations of Lines
Parallel and Perpendicular Lines
Definition:
A.
Two lines are parallel if they have the same slope.
B.
Two lines are perpendicular if their slopes are negative
reciprocals of each other.
Remark: If m1 is the slope of the first line and
Absolute Value Equations
Equations Involving Absolute Values
To solve an equation that involves an absolute value, turn the equation into an "Or"
statement.
Example
Solve
x = 2
Solution
x = 2 or x = 2
Example
x + 1 = 2
Solution
x+1 = 2
x = 1
or
or
x
Assignment of domain of a function
(Math 152A Supplement for 4.6)
Find the domain of the following functions
1)
3
2)
y =
5
3)
y =
x
y = 3x  7
x+1
1)
2)
3)
4)
4x
5)
y =
5x
6)
y = x2  3x + 4
y =
2x + 3
7x  1
4)
5)
6)
7)
7)
y = 3x2  5x + 2
8)
9)
8)
9)
10
The Number Line, Absolute Value,
Inequalities, and Properties of R
The Number Line
To draw a number line we draw a line with several dashes in it and ordered numbers
below the line, both positive and negative. The number corresponding to the point on
the
Arithmetic Of Polynomials
Definition of a Polynomial (Vocabulary)
Definition:
A monomial is a number times a power of x: axn
Examples
3x2,
1/2 x7,
and
8
are all monomials.
Definition:
A polynomial is a sum or difference of monomials
Examples:
4x5  3x2 
Compound Inequalities
And
If we have two sets A and B, then we say that an element belongs to A and B if it
belongs to both of them. For example, a student may belong to the honor society if
that student is a member of A and Bwhere
A = the collection of a