SWHS
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SWHS
4Algebra
1
Review Packet
The purpose of this packet is to identify the topics from
Algebra 1 that you must know to be successful in Algebra 2
and to provide you with some problems to use for practice.
This packet will be collected and you will be tested on this
material within the first 3 weeks of your 4Algebra 2 course.
It is your responsibility to complete this packet and to seek
any help you may need prior to the test. Make sure that you
show all work using proper format.
You may want to consult the following websites for
additional information and practice:
http://www.phschool.com/atschool/ucsmp/algebra/Student_Area/ALG_S_BK_index.html
http://www.algebrahelp.com/
http://www.purplemath.com/modules/index.htm
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TABLE OF CONTENTS
TOPIC
PAGE
1. REAL NUMBERS………………………………………………………………………………………………
3
2. MULTIPLICATION AND DIVISION
3
WITHOUT A CALCULATOR……………….
3. SIMPLIFYING RADICALS……………………………………………………………………………
4
4. ALGEBRAIC EXPRESSIONS…………………………………………………………………………
4
5. SOLVING LINEAR EQUATIONS………………………………………………………………
5
6. SOLVING LINEAR INEQUALITIES…………………………………………………………
6
7. ABSOLUTE VALUE EQUATIONS AND INEQUALITIES…………………….
7
8. REWRITING EQUATIONS AND FORMULAS…………………………………………
7
9. FUNCTIONS…………………………………………………………………………………………………….
8
10. SLOPE……………………………………………………………………………………………………………….
9
11. GRAPHING LINEAR EQUATIONS……………………………………………………………
9
12. WRITING THE EQUATIONS OF A LINE………………………………………………
10
13. SOLVING LINEAR INEQUALITIES IN TWO VARIABLES………………
10
14. RULES OF EXPONENTS………………………………………………………………………………
11
15. MULTIPLYING POLYNOMIALS…………………………………………………………………
11
16. FACTORING…………………………………………………………………………………………………….
12
17. SOLVING SYSTEMS OF EQUATIONS……………………………………………………
12
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1.
REAL NUMBERS AND THEIR PROPERTIES
TERMINOLOGY
Natural Numbers
Whole Numbers
Integers
Rational Numbers
Irrational Numbers
Real Numbers
PRACTICE
1. To which of the above set(s) do each of the following numbers belong:
a.
-2
c.
2
5
d.
8
9
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2.
b.
MULTIPLICATION AND DIVISION
WITHOUT A CALCULATOR
PRACTICE
1.
Perform the following operations without using a calculator.
a.
(245)(163)
b.
3570 17
c.
56088 123
d.
(1234)(5678)
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3.
SIMPLIFYING RADICALS
TERMINOLOGY
Radicand
Simplest form
Product property
Quotient property
Rationalizing the denominator
PRACTICE
1.
Simplify each of the following. Assume all variables represent positive
values.
a.
d.
f.
b.
75x 2
3 2 5 7 2 7 4 7
5
4
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4.
27 2 5 75
e.
g.
6 14
c.
3 25x 3
4
5
ALGEBRAIC EXPRESSIONS
TERMINOLOGY
Expression vs. equation
Algebraic expression vs. numerical expression
Order of operations
Evaluate vs. simplify
EXAMPLE (using expected format)
Evaluate the expression without using a calculator: 56 12 32
56 12 32
56 4 2
56 8
48
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PRACTICE
1. Evaluate each expression for the given value of x:
x 9 2x when x = -3
a.
2.
3x
b.
3
2
5x 2
7x 10
when x = 5
Evaluate each expression without using a calculator.
25 7
3
a.
16 233 11 4 52
b.
3.
Simplify the expression:
3(x 2 2x) 5x(2x 3)
1
5
15 3 2
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5.
SOLVING LINEAR EQUATIONS
TERMINOLOGY
Linear equation
EXAMPLE (using expected format)
Solve and check:
6x – 13 = 22 – x
check;
6(5) – 13 = 22 - 5
7x – 13 = 22
30 – 13 = 17
7x = 35
17 = 17
x=5
PRACTICE
1. Solve each equation. Check your solution. NOTE: If the equation contains
fractions DO NOT change them to decimals.
a.
c.
3x 14 11
1
x 8 3
2
b.
d.
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4x 12 3x 9
6(x 5) 4(x 3) x
3 (2x 9) 17
e.
2.
f.
2
3
x2 x4
3
2
Find the dimensions of the rectangle given that the
20 x - 48
area is 504 sq. units.
7
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6.
SOLVING LINEAR INEQUALITIES
TERMINOLOGY
Inequality symbols (less than, greater than, less than or equal to, greater
than or equal to)
Compound inequality
Multiplying/dividing by a negative number
PRACTICE
1. Solve each of the following and graph the solution on the number line.
a.
3x 9 12
b.
7x 10 11
d.
4 2x 6 8
c.
2
x4 8
3
e.
3x 5 1 or
4x 1 3
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7.
ABSOLUTE VALUE EQUATIONS AND INEQUALITIES
EXAMPLE (using expected format)
3x 2 7
3x 2 7 or 3x 2 7
3x 5 or
3x 9
5
x
or
x 3
3
PRACTICE
1.
Solve each of the following.
a.
4x 6 10
b.
c.
2
6 x 12
3
d.
24x 3 48
22x 1 2
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8.
REWRITING EQUATIONS AND FORMULAS
PRACTICE
1. Solve each of the following equations for y.
a.
6x 3y 9
c.
2xy + 9y = 8
2.
Solve each formula for the indicated variable.
a.
1
A bh for b
2
c.
A r 2 for r
b.
5x y 3
d.
3(2x 4y) 12
b.
9
F C 32 for C
5
d.
p 2(l w)
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for w
9.
FUNCTIONS
TERMINOLOGY
Domain
Range
Function
Function notation
Vertical line test
Linear function
PRACTICE
jx x
1.
Evaluate f x x x 2 when x = -2
2.
Evaluate
3.
2
3
2x 2 when x = 9
Identify whether the relation {(2, -2), (3, 5), (3, 1), (8, 1)} is a function.
Explain why or why not.
4.
a.
Identify the domain and range.
5
-2
b.
Is this a function? Why or why not?
9
6
8
5.
Using the vertical line test, explain why the graph below is or is not a
function.
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10. SLOPE
TERMINOLOGY
Slope (positive, negative, zero, undefined)
Parallel lines
Perpendicular lines
PRACTICE
1. Find the slope of the lines that pass through the following pairs of points.
Identify if the line goes up/down or is horizontal/vertical.
a.
(-2, 4) (4, 8)
b.
(2, 7) (2, -65)
c.
(10, 8) (1, 1)
d.
2 7 15 7
, ,
3 8 17 8
2. Determine if the lines determined below are parallel, perpendicular or neither.
a.
Line A contains (3, 5) and (-7, 1) Line B contains (8, 7) and (6, 2)
b.
Line A contains (3, 5) and (-7, 1) Line B contains (4, -1) and (-1, -3)
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11. GRAPHING LINEAR EQUATIONS
TERMINOLOGY
y-intercept
x-intercept
PRACTICE
1.
Identify the slope and y-intercept of each line.
a.
y = 7x + 9
b.
3x – 5y = -6
c.
y=2
d.
x = -8
2.
Find the x- and y-intercepts of each line.
a.
7x – 8y = 56
b.
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y = 9x + 2
3.
Graph.
a.
2
y x3
3
b.
2x – 5y = 15
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12. WRITING THE EQUATIONS OF A LINE
TERMINOLOGY
slope
y-intercept
PRACTICE
1.
Write the equation, in slope-intercept form, for each of the following lines.
a.
slope = 4, y-intercept = 7
b.
slope =
c.
through (6, -2) and parallel to y = 7x – 1
d.
e.
1
, through (-2, 8)
2
through (6, -2) and perpendicular to y = 7x – 1
through (-1, 7) and (4, 0)
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13. SOLVING LINEAR INEQUALITIES IN TWO VARIABLES
PRACTICE
1.
Graph the solutions to the following inequalities on the coordinate plane.
a.
y 2x 6
b.
2
y x2
3
c.
y 8
d.
2x 3y 9
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14. RULES OF EXPONENTS
TERMINOLOGY
Product of powers
Power of powers
Quotient of powers
Power of a quotient
Zero exponent
Negative exponents
PRACTICE
1. Simplify each expression leaving variables with positive exponents.
a.
b.
4c cd
2
d.
4
8c
4
5 3 4
2
2
0
h.
6m3 n 2
18m5 n
c.
(2x + y)(3x + 4y)
5
ab
4x7x
e.
3
f.
c.
2c 4
5d
3
9c 4
3c 2
3
g.
7x y
2
3
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15. MULTIPLYING POLYNOMIALS
TERMINOLOGY
Polynomial; monomial, binomial; trinomial
FOIL
PRACTICE
1.
Multiply and simplify each of the following.
a.
(x + 1)(x + 4)
b.
(x + 1)(x – 4)
d.
(x + 6)(x – 6)
e.
(x – 2)(3x2 – 6x + 12)
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f.
(3x – 4) 2
16. FACTORING
TERMINOLOGY
Factor
Common monomial factor
Difference of Squares
Perfect Square Trinomial
PRACTICE
1.
Completely factor each of the following.
a.
6x3y + 12x2y2 – 18x
b.
x2 + 11x + 18
c.
2m2 + 22m – 52
d.
4x2 – 9y2
e.
x 2 10 x 25
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17. SOLVING SYSTEMS OF EQUATIONS
TERMINOLOGY
system of equations
solving systems by substitution, elimination (linear combination), and
graphing
PRACTICE
1.
3x 2 y 7
Solve the following system
2x 5y 10
a.
graphing
b.
substitution
c.
elimination (linear combination)
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using
