MHUSD Mid-Year Final Study Guide Algebra 1

MHUSD Mid-Year Final
Study Guide
Algebra 1
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Adding/Subtracting Polynomials: (7-7)
Multiplying Polynomials: (7-8 & 7-9)
EX [1]
EX [2]
You Try!
You Try!
[1] Simplify:
[3] Simplify:
[2] Simplify:
[4] Simplify:
Point-Slope Form
Given a line with slope m,
Passing through the point (x, y):
Linear Equations: (Chp.5)
We write equations three different ways:
Slope-Intercept Form
Standard Form
Given a line with slope m, and
Any line can be represented in the
y-intercept (0, b):
form:
Where A and B, and C are constants,
and A and B are both 0.

To check if a point lies on a line, which means that it is a solution to the linear equation, substitute
the x and y values of the point into the equation, and check for equality.

To identify the x- and y- intercepts of a line:
 at the y-intercept, the value of x is 0, (set x to 0 and solve for y)
 and at the x-intercept, the value of y is 0, (set y to 0 and solve for x)
EX [1]
Is the point (2,-7) a solution to the equation
EX [2]
What is the y-intercept of the following line:
Therefore, the
y-intercept is
Therefore, the point (2, -7) is not a solution to the
equation
You Try!
You Try!
[5]
[6] Is the point
equation :
What is the x-intercept of the line :
A1: Mid-Year Study Guide (Chps.1-7)
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a solution to the linear
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To find the Equation of a line: (5-1)
When you have a point and a slope, use the Point-Slope Formula:
OR substitute the point slope into the Slope-Intercept Formula:
equation in slope-intercept form [see example 2 below].
[see example 1 below].
, solve for b, and rewrite the
EX [1] To find the equation for the line with a slope of
that goes through the point (4, -6).
EX [2] To find the equation for the line that goes
through the point (-5, -7) whose slope is -2.
Use the point-slope formula:
Use the slope-intercept formula:
Substituting -17 in for b in slope-intercept form:
TIP: If you only have two points, use the slope formula to find the slope, then use either method above.
EX [3] Find the equation for the line through the points (-5, 4) and (1, 0).
Use the slope formula:
Now, use the point-slope formula. Use the point
(1, 0) because the numbers are easier to work
with:
You Try!
You Try!
[7] Find the equation for the line with a slope of
that runs through the point (0, -2).
[8] Find the equation for the line that goes through
the points (-7, -3) and (1, -1).
The Distributive Property: (1-6)
You can simplify using both method [1] and [2].
EX [1]
EX [2]
You Try!
You Try!
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Parallel & Perpendicular Lines: (5-7)
 Lines that are parallel have the same slope.
 Lines that are perpendicular have opposite-reciprocal slopes.
 Lines that are collinear have the same equation (same slope and y-intercept).
To solve problems with parallel or perpendicular lines, transform each equation into slope-intercept form,
and compare slopes:
EX [1]
Are the lines below parallel, perpendicular,
or neither?
EX [2] Determine if the lines are parallel,
perpendicular or neither.
Transform both equations to slope-intercept form:
In both lines, m = 4. Therefore, the lines are parallel.
You Try!
[11]
Determine if the lines are parallel, perpendicular,
or neither:
The slopes are opposite reciprocals (when multiplied,
you get -1), the lines are perpendicular.
You Try!
[12]
Write an equation for a line perpendicular to the
line 3x – 2y = 5 that goes through the origin.
Relations: (4-2) A relation is represented by a set of ordered pairs, a table, a graph, or a mapping. A
mapping illustrates how each element of the domain is paired with an element in the range.
Ordered Pairs
Table
Graph
Mapping
x
y
1
-2
0
3
2
5
-4
-3
Functions: A function is a relation where each element of the domain is paired with exactly one element of the range.
Does this mapping
represent a function?
Does this table represent
a function?
This table represents a relation
that is not a function. The
element 2 in the domain is
paired with 11, 12 and 14 in the
range. If you give x = 0,
you cannot determine the
value of y.
Yes, for each element
of the domain has one
corresponding
element for the
range.
You Try!
[13]
x
y
-5
0
0
1
0
10
11
12
13
14
Determine whether each relation is a function.
[14]
A1: Mid-Year Study Guide (Chps.1-7)
[15]
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[16]
[17]
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Solving Multi-Step Equations: (2-3)
EX [1]
Solving Equations w/ Variables on Both Sides: (2-4)
EX [1]


You Try!
You Try!
Real Numbers: (1-2, 1-3, 1-5)
Rational Numbers
Irrational Numbers
Integers
∏
Whole
Numbers
You Try! Name the set(s) of numbers to which each number belongs, and justify the reasoning.
Adding/Subtracting Inequalities: (3-2)
Multiplying/Dividing Inequalities: (3-3)
You Try!
You Try!
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Solving Absolute Value Equations: (2-7)
CASE 1
You Try!
Special Cases of Absolute Value Equations: (2-7)
CASE 2
Solve each equation.
Compound Inequalities Involving AND: (3-6)
There is only one case.
Since 3 is added to x,
subtract 3 from both sides
to undo the addition.
CASE 1
You Try!
Solve each equation.
Compound Inequalities Involving OR: (3-6)
You Try!
Integer Exponents: (7-1)
Multiplication & Division Properties of Exponents: (7-3)
You Try!
You Try!
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System of Linear Equations: (6-1, 6-2, 6-3,6-4)
You Try!
Solve each system of linear equations. Classify each system. Give the number of solutions.
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