2.2 An Introduction to Problem Solving
Consecutive Integers: Integers that follow one another
2, 3, 4
13, 14, 15
x, x+1, x+2
5, 6, 7
25, 26, 27
Consecutive Odd Integers: Odd integers that follow one another
3, 5, 7
9, 11, 13
x, x+2, x+4
Consecutive Even I
2.3 Formulas and Problem Solving
Formula: an equation that describes a known relationship among
quantities.
Formula:
I = PRT
A = lw
d = rt
c = 2 r
v = lwh
Ex 1 Solve d = rt for r.
See page 75 Solving Equations for Specified Variable
Ex 2 Solve 2y + 5x = 1
2.1 Linear Equations in One Variable
Equations: a statement that two expressions are equal
Solution: a value that makes the equation a true statement
Solving an equation: the process of finding the solution to an equation
First Degree Equation: a linear e
Math 096
Practice Exam 4
Name_
You must show work for credit. Each question is worth 5 points for a total of 105 points.
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Findthesquareroot.Assumethatallvariablesrepresentp
2.4 Linear Inequalities and Problem Solving
Linear Inequalities in One Variable
ax + b < c
where a, b, and c are real numbers, a 0.
You can also use >, , or .
Solution of an Inequality: a value of the variable that makes the inequality
a true statement.
S
2.5 Compound Inequalities
Compound Inequalities: inequalities joined by the word and or he word or
2x + 3 < 5 and 4x 2 > -8
3
x 7 or x + 4 < 5
2
Intersection: an inequality formed by the word and.
The solution of the inequality is the intersection of the
3.3 Graphing Linear Functions
y=x+2
x
-2
0
1
y=x+2
Ex 1 Graph f(x) = 3x and g(x) = 3x 4 on the
same set of axes.
A linear function is a function that can be written in the form: f(x) = mx + b.
Ex 2 Graph f(x) = -1/2 x and g(x) = -1/2 x + 3
on the same set
3.4 The Slope of a Line
Slope: the ratio of vertical change to horizontal change.
(x2, y2)
vertical
change
(x1, y1)
horizontal change
Slope: m =
=
y 2 y1
x 2 x1
where x1 x 2
Ex 1 Find the slope of the line containing the
points (-1, -2) and (2, 5). Graph
3.2 Introduction to Functions
Relation: a set of ordered pairs
Domain: set of all first components of the ordered pairs
Range: Set of all second components of the ordered pairs
Ex 1 Determine the domain and the range.
a) cfw_ (1, 6), (2, 8), (0, 3), (0, -
3.1 Graphing Equations
Rectangular Coordinate System- also known as the Cartesian
Coordinate System
y axis (ordinate)
Quadrant II
Quadrant I
Quadrant III
Quadrant IV
x axis (abscissa)
Plotting: Graphing through a description of its position in terms of di
2.6 Absolute Value Equation
|a| = the distance a is from the origin, 0.
This is always a positive value.
Solving Equations of the form |x| = a
If a is a positive number, then |x| = a is equivalent to x = a or x = -a.
Ex 1 Solve |y| = 5
Ex 2 Solve |4x + 2|
2.7 Absolute Value Inequalities
Solving Absolute Value Inequalities of the form |x| < a
If a is a positive number, then |x| < a is equivalent to a < x < a.
Ex 1 Solve |x| < 4
Ex 2 Solve |x -2| 1
Ex 3 Solve |2x 5| + 2 9
Ex 4 Solve |5x +
2
| -4
7
Solving Ab