Download ALGEBRA II – SUMMER PACKET

NAME ______________________________
DUE: FRIDAY, SEPTEMBER 11, 2009
BASIC ALGEBRA PRELIMINARY ASSESSMENT
Students entering Basic Algebra are expected to recall mathematics skills taught in their
middle school math classes. To review these basic concepts prior to beginning the course,
the mathematics department has prepared the following packet to review those skills.
For each skill, the packet contains several examples, links to online tutorials, and practice
problems for you to complete. The packet is also divided into two parts: one part without
a calculator and one part using a calculator.
SINCE
THIS MATERIAL IS A REVIEW, YOU ARE RESPONSIBLE FOR COMPLETING THIS PACKET ON
YOUR OWN.
IF
YOU NEED ASSISTANCE, YOU MUST COME FOR EXTRA HELP.
There will be an in-class assessment within the first few weeks of school. Prior to taking
the test, this packet will be collected and graded by the teacher to evaluate your efforts
to recall this information. Be sure to SHOW ALL WORK to receive credit.
NO WORK = NO CREDIT!!
PART I – NO CALCULATOR
Complete all the problems in the PRACTICE sections without using a calculator.
SHOW ALL WORK!!
I.
THE NUMBER LINE
Practice – Plot the given set of numbers on the number line.
1)
{ -3, -1.3, 0, 1.5, 4 }
2)
{ -2.3, 
5
4
, 1, 4.03 }
Basic Algebra Preliminary Assessment
QuickTime™ and a
decompressor
are needed to see this picture.
QuickTime™ and a
decompressor
are needed to see this picture.
1
II.
GRAPHING INEQUALITIES
Tutorials:
http://www.sparknotes.com/math/algebra1/inequalities/section4.rhtml
http://www.onlinemathlearning.com/algebra-inequalities.html
Practice - Graph each of the following inequalities on a number line. RECALL: Use an open
OR closed circle and then shade correctly.
1)
x3
QuickTime™ and a
decompressor
are needed to see this picture.
2)
x > -1
QuickTime™ and a
decompressor
are needed to see this picture.
III.
PLOTTING
Tutorial:
ON THE
COORDINATE PLANE
http://www.math.com/school/subject2/lessons/S2U4L1GL.html
Practice - Plot each of the following points on the coordinate plane below. Be sure to
label the grid and label the points with the correct letter after you plot them.
A (3, 6)
B (-2, 5)
C (-4, -2)
D (5, -3)
E (0, 5)
F (2, 0)
G (-3, 0)
H (0, -4)
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IV.
OPERATIONS
WITH
INTEGERS
Tutorials:
http://www.regentsprep.org/Regents/math/ALGEBRA/AOP3/indexAOP3.htm
http://www.aaamath.com/g65-add-3-negative.html
Practice - Evaluate the following using your knowledge of positive and negative numbers.
SHOW WORK AND DO NOT USE A CALCULATOR!!
1)
-13 + 18 = _________
2)
(-6)(-2)(3) = _________
3)
8 – (-4) – 19 = _________
4)
6 + -12 = _________
5)
3(-2)(-1)(-1)(4) = _________
6)
-3 – 12 + (-8) = _________
7)
-8 – 3 + 10 = _________
8)
-28  -2 = _________
V.
ABSOLUTE VALUE
Tutorials:
http://www.regentsprep.org/Regents/math/ALGEBRA/AO7/indexAO7.htm
http://www.coolmath.com/algebra/Algebra1/05AbsValueEq/01_review.htm
Practice - Evaluate the following absolute value problems.
1)
| -16.5 |
2)
|5|
4)
- | - 13 |
5)
| 8 – 17 |
Basic Algebra Preliminary Assessment
3)
- | 18 |
3
VI.
EXPONENTS
Tutorial:
http://www.regentsprep.org/Regents/math/ALGEBRA/AO5/LExp.htm
Practice - Evaluate each of the following. SHOW WORK AND DO NOT USE A
CALCULATOR!!
1)
VII.
43
2)
62
3)
104
4)
91
SIMPLIFYING VARIABLE EXPRESSIONS
Tutorials:
http://www.classbrain.com/artteensb/publish/distributive_property.shtml
http://www.algebrahelp.com/lessons/simplifying/distribution/
http://www.algebrahelp.com/lessons/simplifying/combiningliketerms/
Examples
1)
6x + 9y – 2x – 12y
6x + 9y – 2x – 12y
Combine the terms with x’s and combine the terms with y’s.
4x – 3y
2)
7 (8x + 3)
7(8x) + 7(3)
56x + 21
Distribute the 7 to both terms in the parentheses.
Practice - Simplify each expression by distributing and/or combining like terms.
1)
4x + 7y – 14x + 2y
2)
5 (x + 3)
3)
-3 (2x – 5y)
4)
-13 – 4y – 5z + 15 – (-4z) + 11y
5)
7 (4y – 8m)
6)
20xy + 3x2y – 10x2y – 30xy
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PART II – WITH CALCULATOR
Complete each of the following questions. You may use a calculator. Show all work!!
VIII.
FRACTION OPERATIONS
Examples
Adding & Subtracting Fractions – To add and subtract fractions, you must have a
common denominator – preferably a least common denominator (LCD).
Example 1
1
2

7
The least common denominator for 2 and 8 is 8.
8
1 (4)
2 (4)

7
Multiply the denominator of the first fraction by 4 to
8
create the common denominator of 8 and multiply the
numerator by 4 also.
4
8
Example 2
4
5


7
8
=
11
Add the numerators.
8
2
The least common denominator for 5 and 3 is 15.
3
4 (3)
5 (3)

2 (5)
3 (5)
Multiply the numerator and denominator of the first
fraction by 3 to create the common denominator.
Multiply the numerator and denominator of the second
fraction by 5 to create the common denominator.
12
15

10
15
=
2
15
Add the numerators.
Basic Algebra Preliminary Assessment
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Multiplying Fractions – To multiply two fractions, multiply the numerators and multiply
the denominators. Then simplify the result.
Example 1
Example 2
1
8

4
2 5
4
10
Multiply the numerators and the
denominators.
9
6
8 6

9 1
Simplify the fraction.
48
2
9
5
Rewrite 6 as
6
1
.
Multiply the numerators and the
denominators.
Simplify the fraction.
16
3
Dividing Fractions – To divide two fractions, rewrite the problem as multiplication by the
reciprocal. Follow the rules for the multiplying fractions.
Example
7

10
7

5
6
6
10 5
42
50
Rewrite the problem as first fraction being multiplied by
the reciprocal of the second fraction.
Multiply the numerators and the denominators.
Simplify the fraction.
21
25
Mixed Numbers – Rewrite mixed numbers as improper fractions and proceed with the
operations as described above.
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Practice - Perform the indicated operation.
1)
3)
5)
7)
2
7

3
4
3 2

8 7
16
3
8
1 5
3 
2 8
Basic Algebra Preliminary Assessment
2)
4)
5
12
3
14


1
5
6
7
6)
1
4
2 5
3
5
8)
2
3 2

4 3
7
IX.
CONVERSIONS
Tutorial:
BETWEEN
FRACTIONS, DECIMALS,
AND
PERCENTS
http://www.purplemath.com/modules/percents.htm
Examples
Fraction
Decimal
Percent
GIVEN:
Divide the numerator by the
denominator.
Move the decimal point two
places to the right (multiply
by 100).
1
2
0.5
Since 5 is the last digit in
the thousandths place, put
875 over 1000 and simplify
the fraction.
GIVEN:
0.875
875
1000

100

Move the decimal point two
places to the right (multiply
by 100).
87.5%
7
8
Since 2 is the last digit in
the hundredths place, put 2
over 100 and simplify the
fraction.
2
50%
Move the decimal two places
to the left (divide by 100).
1
0.02
GIVEN:
2%
50
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Practice - Complete the following table. Convert fractions, decimals, and percents.
Fraction
Decimal
Percent
5
1
8
2
0.8
3
70%
8
4
3
5
3.5%
6
0.04
7
4
1
5
8
0.9%
Practice - Compare each of the following pairs of numbers using >, <, or =.
9)
12)
3.398 ______ 3.349
5
8
______
4
6
10)
13)
Basic Algebra Preliminary Assessment
1
5
3
2
______
______
1
11)
6
2
8
______
1
4
4
6
9
X.
ORDER
OF
OPERATIONS (PEMDAS)
Tutorials:
http://www.regentsprep.org/Regents/math/ALGEBRA/AOP2/indexAOP2.htm
http://www.math.com/school/subject2/lessons/S2U1L2GL.html
Parentheses
Exponents
Multiplication 
Done from left to right
Division


Addition
Done from left to right
Subtraction 
Practice – Simplify using the order of operations. Show all work!!
1)
24  4 + 32
2)
14  7  5 - 32
3)
13 + ( 3  2 )2 – 8
4)
5 + [ 30 – ( 6 – 1 )2 ]
5)
[82–(3+9)]+[823]
Basic Algebra Preliminary Assessment
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XI.
EQUATIONS
Tutorials:
http://www.regentsprep.org/Regents/math/ALGEBRA/AE2/LSolvEq.htm
http://www.regentsprep.org/Regents/math/ALGEBRA/AE2/PSolvEq.htm
http://www.coolmath.com/algebra/algebra-practice-solving.html
Practice – Solve each of the following equations. Show all work!!
1)
x–4=2
4)
w+
7)
5x + 2 = 2
2
3
=
5
6
2)
11 + b = 18
3)
5)
-7a = -49
6)
8)
4x – 3 = 17
9)
Basic Algebra Preliminary Assessment
4x = 48
m
6
= -3
-7 = 47 – 6k
11