Download Evaluating Expressions

Sterling Middle School
Review Packet for Rising Algebra I Students 2016
This assignment should be completed without a calculator. All work must be shown for each problem. The
problems should be done correctly, not just attempted.
If you need resource materials, your old notebooks and workbooks are the best references. The
following websites are also good resources if you need a little help remembering:
www.analyzemath.com, www.purplemath.com, www.sosmath.com
Have a great summer, and we will see you in September!
Sterling Middle School Algebra Teachers
Evaluating Expressions
Example
Evaluate the following expression when x = 5
Rewrite the expression substituting 5 for the x and simplify.
Expression
a. 5x =
Substitute for x and Simplify
5(5)
b. -2x =
-2(5)
-10
c. x + 25 =
5 + 25
30
d. 5x – 15 =
5(5) – 15 = 25 – 15
10
e. 3x + 4 =
3(5) + 4 = 15 + 4
19
Practice: Evaluate each expression given that
Expression
1. 3x
2. 2x2
3. 3x2 + y
4. 2(x+2) – y
x=6
y = -1
Substitute values and simplify
Answer
25
z = -6
Answer
5.
6. 5x – (y + 2z)
7. xy + z
8. 2x + 3y – z
Graphing
Points in a plane are named using two numbers, called a coordinate pair. The first number is called the
xcoordinate. The x-coordinate is positive if the point is to the right of the origin and negative if the point is to
the left of the origin. The second number is called the y-coordinate. The y-coordinate is positive if the point is
above the origin and negative if the point is below the origin.
y
The x-y plane is divided into four quadrants (four sections) as described
below.
Quadrant
Quadrant
All points in Quadrant 1 have a positive x coordinate and a positive y coordinate (+x, +y).
2
1
All points in Quadrant 2 have a negative x coordinate and a positive y coordinate (-x, +y).
(+x, +y)
(-x, +y)
All points in Quadrant 3 have a negative x coordinate and a negative y coordinate (-x, -y). All
points in Quadrant 4 have a positive x coordinate and a negative y coordinate (+x, -y).
The origin is (0, 0).
x
• Origin
Quadrant
3
(-x, -y)
Quadrant
4
(+x, -y)
2
Plot each point on the graph below.
Determine the coordinates for each coordinate
point below.
1. A (-6,2)
2. B (4,0)
9. A (5, -5)
3. C (4,-7)
4. D (-3,-1)
11. C (
,
5. E (0,7)
6. F (-4, 8)
13. E (
7. G (6, 2)
8. H (-8, -9)
15. G (
Example: A (-6, 2)
10. B (
,
)
)
12. D (
,
)
,
)
14. F (
,
)
,
)
16. H (
,
)
Example: A (5, -5)
F
•
B
E
A
•
•
•
D
C
• •
G
•
A
•
H
•
3
Complete the following tables. Then graph the data on the grid provided.
4
Solving Equations
To solve an equation means to find the value of the variable. We solve equations by isolating the variable using
opposite operations.
Opposite Operations:
Addition (+) & Subtraction (-)
Example: Solve 3x – 2 = 10
Multiplication (x) and Division (÷)
3x
-2=
10
+2
+2
Isolate 3x by adding 2 to each side
Please remember…
3x
=
12
To do the same step on each side of the
3
3
Isolate x by diving each side by 3
equation
X
=
4
Simplify
Check your answer.
3(4) - 2 = 10
12 – 2 = 10
10 = 10
Substitute the value in for the variable
Simplify
Is the equation true? If yes, you solved it correctly!
Always check your work
by substitution!
Practice: Solve and check. Show your work!
1. x + 3 = 5
2. w – 4 = 10
3. y – 5 = -8
4. 3p = 9
5. -7k = 14
6. –x = -17
8.
9. 2x + 11 = 9
7.
10. 2x – 5 = 11
11. 4n + 1 = 9
12. 5j – 3 = 12
13. -6x + 3 = -9
5
Inequalities
An inequality is a statement containing one of the following symbols:
< is less than
> is greater than
≤ is less than or equal to
≥ is greater than or equal to
The graph of an inequality with one variable is the set of points that represent all solutions of the inequality. To
graph the solution to an inequality with one variable:
Use an open circle
ο
for
<
and
>
Use a closed circle
• for
<
and
>
Examples:
X>0
-2
-1
0
1
2
- 14
- 11
-8
-5
-2
X≥8
Practice: Graph each of the following inequalities
on a number line.
1)
2)
4)
3)
W
Practice: Write an inequality for each graph.
5)
7)
6)
8)
6
7