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```									                       ALGEBRA 1 FINAL EXAM REVIEW PACKET 2012

FINAL EXAM REVIEW: Chapter 6                 Solving Linear Inequalities

Required Skills:       1)   Solve an inequality using addition, subtraction, multiplication or
division.
2)   Solve a multi-step inequality
3)   Graph the solution to an inequality on a number line.
4)   Solve a compound inequality and graph solution on a number line.
5)   Solve open sentence equalities and inequalities involving absolute
value. Graph solution on a number line.
6)   Solve absolute value equations
7)   Graph absolute value functions
8)   Describe the shifts in an absolute value function given its equation
9)   Graph a linear (2-variable) inequality on the coordinate plane.

Problems

I.   Solve each inequality. Write your answer using set-builder notation (e.g., {x | x > 1}).

1)   -23  g – 6                                 2)   9p  8p – 13

7
3)   d – 5  2d – 14                             4)       w ³ - 21
8

f -5
5)   -3 (k – 2)  12                             6)           >- 3
3

7)   4m – 11  3m + 7                            8)   -22b  99

Algebra 1/MD/6-12                                                                           1
II. Solve each compound inequality. Then graph the solution set on a number line.

1)   r + 3  2 and 4r  12

2)   3n + 2  17 or 3n + 2  -1

3)   -1  p + 3  5

III. Solve each open sentence. Then graph the solution set.

1)    k +5 = 2

Algebra 1/MD/6-12                                                                   2
2)    2a -5 <7

3)     7-3s ≥ 2

IV. Solve each equation.

1)   |q+5|=2               2)   | 5c – 8 | = 12

5h + 2
3)              =7         4)   | 6r + 8 | = -4
6

Algebra 1/MD/6-12                                 3
V.   Graph each function.

1
1)   y=|x+2|-3              2)   y=       |x–1|+2
2

VI. Graph the inequality.

1)   y  5x + 1             2)   x + 2y  4

Algebra 1/MD/6-12                                   4
FINAL EXAM REVIEW: Chapter 7                  Solving Systems of Linear Equations

Skills:    1)       Identify if an ordered pair is a solution to a system of equations.
2)       Determine whether a system of equations has zero, one, or infinitely many
solutions. Be able to describe system as consistent, inconsistent, dependent,
independent
3)       Solve a system of equations by graphing.
4)       Solve a system of equations by substitution.
5)       Solve a system of equations by elimination.
6)       Determine the best method for solving systems of equations.
7)       Solve a system of inequalities by graphing
8)       Write and solve a system of equations to solve an application problem

I.   Determine if the given point is a solution of the system.

1)   Is (3, -2) a solution to:                    2)   Is (-6, 8) a solution to:

ì-3x + 4y = -17                                   ì 2x + y = 4
í                                                 í
î 4x + 5y = 2                                     î5x + 3y = 6

II. Graph each system and identify the solution (if there is one).

ìx + 2y = -4                                      ì-2x + y = 3
7)    í                                           8)    í
î3x - y = -5                                      î6x - 3y = 6

Algebra 1/MD/6-12                                                                            5
III. Solve each system of equations by any method.

ì y = 3x                                ì x = 4 + 6y
1)    í                                  2)   í
îx + y = 4                              î3x - 18y = 4

ì x - 5y = 10                           ì2x - 5y = -16
3)    í                                  4)   í
î2x - 10y = 20                          î -2x + 3y = 12

ì 2x + 5y = 3                           ì 2x - 3y = 1
5)    í                                  6)   í
î-x + 3y = -7                           î5x + 4y = 14

ì y = 3x - 4                            ì 8x - 3y = 10
7)    í                                  8)   í
î6x - 5y = 38                           î5x + 4y = -29

Algebra 1/MD/6-12                                               6
IV. Solve each system of inequalities by graphing.

ìy < - x +1
ï                                           ìx ³ 2
ï
1)    í                                      2)   í
îy £ 2x + 3
ï                                           îy + x £ 5
ï

V.     Write a system of equations and solve.

1)     Adult tickets for the school musical sold for \$3.50 and student tickets sold for
\$2.50. 321 tickets were sold altogether for \$937.50. How many of each kind of
ticket were sold?

Algebra 1/MD/6-12                                                                         7
FINAL EXAM REVIEW: Chapter 8                   Polynomials

Required Skills:        1)    Multiply monomials.
2)    Simplify expressions involving powers of monomials.
3)    Simplify expressions involving quotients of monomials.
4)    Simplify expressions containing negative exponents.
5)    Express numbers in scientific notation.
6)    Express numbers in standard notation.
7)    Find the degree of a monomial.
8)    Classify a polynomial.
9)    Write a polynomial in ascending and descending order.
10)   Find the degree of a polynomial.
11)   Add and subtract polynomials.
12)   Find the product of a monomial and a polynomial.
13)   Multiply two polynomials.
14)   Solve problems by writing a polynomial to represent the situation

I.    Evaluate each of the following.

1)    46                              2)   (-3)4                         3)   (12.1)3

II.    Express each of the following in standard notation

1)    8.12 x 104                      2)   1.105 x 10-6                  3)   3.7 x 103

III. Express each of the following numbers in scientific notation.

1)    0.00137                         2)   587020000                     3)   0.00791

IV.    Evaluate. Express the result in scientific notation.

7          -8                         2.142 x 10-4
1)     (3.5 x 10 ) (6.1 x 10 )                     2)
5.1 x 102

Algebra 1/MD/6-12                                                                            8
V.     Determine the degree of each monomial.

1)   7m11n9                                          2)   14x2y7z

VI. Determine the degree of each polynomial.

1)   7x3 – 9x + 11                                   2)   27m23n14 – 9m11n31

VII. Perform the indicated operation.

1)   (3x2 - 4x + 1) + (-8x2 + 7x - 3)                2)   (7x2 + 3x - 9) + (-5x2 - x + 1)

3)   (5x2 - x + 8) - (2x2 + 3x - 1)                  4)   (-7x2 + x - 3) - (-5x2 - x + 4)

VIII. Simplify each of the following expressions.

1)   (3x2y)(-2x5y2)                   2)   (x2y3)4                       3)    (3x2y)2

3         2 3                    30x5                                -21y 8
4)   (-4x y)(2x y )                   5)                                 6)
5x3                                 28y11

Algebra 1/MD/6-12                                                                           9
a -5
7)    (4x2y3)0            8)   (-7y3x0)(2x4)                  9)
b -7

x -5z -3
10)                       11) -(3x2 - 8)                      12) 11a2 - 4a + a - 16a2
xz7   -11

IX. Find each product.

1)    2x (3x2 - 4x + 1)                2)   6y3 (3y4 – 11y2 – 7y)

3)    (x + 3)(x - 7)                   4)   (x - 9)(x + 9)

5)    (y + 7)2                         6)   (3y + 1)(y - 2)

7)    (2y + 5)(3y + 1)                 8)   (7y – 4)(4y + 6)

9)    (3x - 4)2                        10) (2x + 7)(3x2 – 4x + 2)

Algebra 1/MD/6-12                                                                    10
X.    Solve.

1)   Find the simplest expression for the perimeter of the triangular roof truss.

2)   An office supply company produces yellow document envelopes. The envelopes come in
a variety of sizes, but the length is always 4 centimeters more than double the width.
Write a polynomial expression to give the perimeter of any of the envelopes.

3)   Suppose a quilt made up of squares has a length-to-width ratio of 5 to 4. The length
of the quilt is 5y inches. The quilt can be made slightly larger by adding a border of 1-
inch squares all the way around the perimeter of the quilt. Write a polynomial
expression for the area of the larger quilt.

Algebra 1/MD/6-12                                                                        11
FINAL EXAM REVIEW: Chapter 9              Factoring

Required Skills:    1)   Write the prime factorization of a number.
2)   Identify the factors of a number.
3)   Determine the greatest common factor of two monomials.
4)   Factor a polynomial using the greatest common factor.
5)   Factor a trinomial with a leading coefficient of 1.
6)   Factor a trinomial with a leading coefficient other than 1.
7)   Factor the difference of perfect squares.
8)   Identify the sum of perfect squares as prime.
9)   Solve application problems, such as factors or gcf, vertical motion,
area

I.   Write each of the following numbers as a product of primes.

1)   250                                      2)   -345

II. Identify all the factors of each number.

1)   28                                       2)   225

Algebra 1/MD/6-12                                                                       12
III. Find the missing factors.

1)   a11  _______ = a23                2)   a7b3c4  _______ = a11b4c18d9

3)   -4y3  _______ = -48y7             4)   -11x5y2  _______ = 22x8y2

5)   _______  6mp8 = -42m6p13          6)   8d6wz7  _______ = 48d6w5z16

IV. State the greatest common monomial factor.

1)   16 and 44                          2)   24 and 36

3)   25x9 and 90x12                     4)   20y7w9 and 28y5w

V.   Factor completely (if possible).

1)   3x2 + 27x + 9                      2)   b4 – 3b3 + 7b2

3)   4y3 + 40y2 + 24y                   4)   14a5w6 – 49a4w5 + 28a2w7

Algebra 1/MD/6-12                                                            13
5)    x2 + 5x + 6       6)    x2 – 25

7)    y2 + y – 12       8)    a2 – 7a – 18

9)    w2 + 36           10) 3xy – 4x + 6y – 8

11) 2x2 + 23x + 45      12) 4x2 - 4x – 3

13)    5x2 - 10x + 5    14)    4x3y - 2x2y - 2xy

15) 4y2 + 4y – 35       16) 6u2 – 13u - 15

17)    2x2 + 16x + 30   18)    2x2 - 32x

Algebra 1/MD/6-12                                  14
VI. Solve each equation.

1)     (3n + 2) (n – 2) = 0   2)   16y2 – 8y = 0

3)     x2 = x + 110           4)   8n2 + 4 = 12n

5)     36x2 + 49 = 84x        6)   4y2 + 16y + 7 = 0

7)     49w2 – 25 = 0          8)   5d3 – 80d = 0

Algebra 1/MD/6-12                                      15
VII. Write a let statement and equation, then solve.

1)     Julian kicked a soccer ball into the air with an initial upward velocity of 40 feet per
second. The height, h, in feet of the ball above the ground can be modeled by
h = -16t2 + 40t, where t is the time in seconds after Julian kicked the ball. Find the
time it takes the ball to reach a height of 25 feet above the ground.

2)     The length of a rectangle is five times the width. The area is 125 square
centimeters. Find the dimensions of the rectangle.

3)     The product of two consecutive even integers is 224. Find their sum.

4)     Ms. Baxter wants to tile a wall to serve as a splashguard above a sink in the
basement. She plans to use equal-sized tiles to cover an area that measures 48
inches by 36 inches. What is the maximum-size square tile Ms. Baxter can use and
not have to cut any tiles? How many tiles of this size will she need?

Algebra 1/MD/6-12                                                                         16
FINAL EXAM REVIEW: Chapter 11                   Radical Expressions

Skills:        1)   Simplify square roots, including with variables
2)   Multiply and divide square roots
3)   Rationalize the denominator of a radical expression
4)   Ensure a radical expression is in simplest radical form
5)   Add, subtract, and multiply radical expressions
6)   Solve radical equations
7)   Apply the Pythagorean Theorem

I.   Simplify.

1)        68                                       2)    28a 6b3

147x3                                          10   4
3)                                                 4)       ·
y2                                          3   30

1
5)                                                 6)    5 · 20
2

7)    2 27 + 63 - 4 3                              8)    6 · æ 4 + 12 ö
è        ø

Algebra 1/MD/6-12                                                             17
æ 1 - 3 ö æ 3+ 2 ö                             2
9)                                        10)   6+
è       øè       ø                             3

2                                    1-2 5
11)                                       12)
3 +     6                               4 + 3 2

II. Solve each equation. Check your solution.

1)     a = 10                             2)    x + 3 = -5

3)    3 + 5 n = 18                        4)     4b + 1 - 3 = 0

5)     3x + 12 = 3 3                      6)    2c - 4 = 8

Algebra 1/MD/6-12                                                 18
FINAL EXAM REVIEW: Chapter 12                   Rational Expressions and Equations

Required Skills:         1)    Identify excluded values of the domain of a rational expression
2)    Simplify a rational expression
3)    Multiply and divide rational expressions

I.   Identify restrictions on the domain and then simplify.

n2 - 3n                                              a 2 - 25
1)                                                 2)
n-3                                              a 2 + 3a - 10

x2 + 10x + 21                                      x2 + x - 20
3)                                                 4)
x3 + x2 - 42x                                        x+5

II. Find each product or quotient.

3a - 6         a+3                                2m2 + 7m - 15       9m2 - 4
1)              i                                  2)                   ¸
a2 - 9        a 2 - 2a                                 m+5            3m + 2

Algebra 1/MD/6-12                                                                            19

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