Math 1310 Review Section 0
1.1 Sets and the Structure of Algebra
Integers (positive, negative, zero):
Prime Numbers: only integer factors are itself & 1
Rational Numbers:
numerator
where both are integers; the denominator can not be zero.
deno min ator
They can also be depicted as terminating or repeating decimals. On tests they will be reduced
6
)
8
7 , but not 3 . 8 .
(otherwise they are incorrect, e.g.
1.2
1.3
1.4
2.1
Irrational Numbers: Π , e,
2 , 4
Real Numbers: Union of Rational and Irrational
Absolute Value: identified by | |, never negative
Compare Numbers: > , = , <
Operations with Real Numbers
Additive Identity is 0
Multiplicative Identity is 1
When multiplying a number of terms
odd number of negatives = even number of negatives = +
Divide & Multiply are interconnected. 6 divided by 3, means find which number multiplied by 3 is 6
Note: You CANNOT DIVIDE BY 0. n/0 (n≠0) is undefined; 0/0 is indefinite.
Exponent, Roots, and Order of Operations ( OOO )
-2 4 = -16
( -2 ) 4 = +16
Order of operations:
parentheses (inner first)
powers (exponents)
÷, × (left to right)
-, + (left to right)
Note: ( x + y ) 2 ≠ x 2 + y 2
Evaluating and Rewriting
Translate words to expressions
Read the whole problem to get general ideas
Read again, converting phrases to find out what you know
Read again to determine what you need
Determine equation to use
Solve the equation
Write solution (including units)
Check if the solution fits
Linear Equations and Formulas
Solve linear equations
clear parenthesis
simplify both sides (combine terms)
move variable to the left side
if variable still exists
move constant to the right side
divide both sides by coefficient of variable
else
if constants are equal, infinite solutions
if constants are not equal, no solution
endif
2.2 Solving Problems (very similar to 1.4)
Word problems (rewrite of method in 1.4)
read for understanding
determine what you know
determine what you need to find
determine what formula to use solve
identify solutions (don’t forget units)
check to see if solution is OK
2.3 Solving Linear Inequalities
Number line -4 -3 -2 -1 0 1 2 3 4
| | | | | | | | |
Inequalities are solved the same way as equalities, with one difference - if the coefficient of the variable is
negative, reverse the direction of the inequality.
Inequalities
in set notation e.g. { x | x > 2 }
in interval notation e.g. ( 2, ∞ )
visually e.g. -4 -3 -2 -1 0 1 2 3 4
| | | | | | ( | |
2.4 Compound Inequalities
Interval(s) Solution
Bounded both above and below (AND)
e.g. 3 < x < 8
( 3, 8 ] or ( 3, +∞ ) ∩ [ 8, + ∞ )
Split intervals (OR)
e.g. x < -4 or x > 1
( -∞, -4 ) U [ -1, +∞ )
3.1 Graphing Linear Equations
Cartesian coordinate system
axis
origin
identifying points
intercepts
graphing a linear equation
intercepts
solve for y, and use values for x