Download Intermediate Algebra Final Exam Review Packet 2009

NAME: ___________________
2015 ALGEBRA II
FINAL EXAM REVIEW PACKET
Start studying now! You should be able to do all problems in this packet on your own.
Remember, there are full video solutions to this packet on the Final Review website.
This review is worth 20 pts. on your final & should be turned in on the day of the final.
Final Exam Date & Time: Friday, June 12th from 8:00-10:00
You must bring your own calculator & pencils
Part I – Solving Systems of Equations by Graphing
Graph each equation and write the solution of each. Write the solution as an ordered pair, or indicate no
solution or infinite solution.
1.)
2x + 2y = 12
y = 2x
Solution:_________________
2.)
y=
2
x–5
3
3y – 2x = 4
Solution:__________________
Part Ib- Graphing Systems of Inequalities
a.)
x  –3
b.)
x + 3y > 6
4x – 3y < 9
5x + 3y
–9
y < –9
Part II – Solving Systems of Equations by Substitution
1) x = 3y + 3
2x + 9y = 11
Part III – Solving Systems of Equations by Elimination
1) x – y = 6
2x + 9y = 1
2) 3x + 4y = -7
2x + y = -3
2) x – 2y = 5
2x + 2y = 7
Part IV—Matrices
Perform the indicated operation.
1.
é -3 6 ù é 2 -1 ù
ê
ú+ê
ú=
êë -9 12 úû êë 9 0 úû
3.
é 1 2 -1 3 ù
ú=
2ê
êë 0 -2 4 5 úû
2.
é 4 2 ù é -2 4 ù
ê
ú-ê
ú=
êë -9 0 úû êë -5 1 úû
Solve the following system using matrices on your graphing calculator. First, write the augmented matrix
(the one you will plug into your calculator), then write your solution as an ordered triple.
ì3x + y + 2z = -1
ï
í-2x + 3y + z = -9
ï 4x - y - z = 7
î
Write a system for the given word problem. Solve using matrices on your graphing calculator. Be sure to
define your variables, write two separate equations, rewrite the system as a matrix, and state your answer
in a complete sentence.
Tickets to a school play cost $3 for students and $5 for adults. If there were a total of 100 tickets sold, making
$420, how many of each ticket were sold?
Part V – Special Right Triangles
Part VI – Right Triangle Trigonometry
1)
Use right triangle trigonometry (SOH CAH TOA) to find the unknown side lengths in the triangle.
a)
b)
A
B
27o
A
B
42o
9
C
16
C
2)
Use inverse trig functions (like sin-1) to find the measures of the missing angles in each triangle.
a)
A
15
C
B
b)
27
9
B
A
6
C
3) You are building a ramp to help your grandmother get in an out of the house. Regulations indicate that the
angle of elevation on ramps be 9. If the front door is 3 feet high, how many linear feet of wood do you need
to build the ramp?
Part VII – Radicals (including imaginary numbers)
Simplify the following completely.
1.
4.
7.
24
27
3
2.
3 60
3.
5.
7 -12
6.
5
8.
3+ 2
5
4
5 2
3
9
4i
Add or subtract the following radicals. Simplify completely.
9.
-4 2 + 5 2
10.
6 5 - 125
11.
4 8 + 2 24
Multiply the following. Simplify completely.
12.
-4 æ -2 5 ö
è
ø
13.
-3 5 i 2 8
14.
2 6 æ 2 + 8 3ö
è
ø
15.
æ3 2 - 5ö
è
ø
2
Part VIII – Solving Radical Equations
Solve each of the following for x.
1.
x+4 -5= 7
2. 2 x - 3 = 8
3.
Part IX – Factoring Trinomials with a Leading Coefficient of 1
a)
x2 – 7x + 6
b)
m2 + m – 42
Part X – Factoring Trinomials with a Leading Coefficient Other Than 1
a)
3a2 + 7x + 2
b)
4y2 + 3y – 1
1
x-5 = 2
4
Part XI – Factoring Difference of Perfect Squares
a)
x2 – 16
b)
4b2 – 81
d)
18x3y - 27xyz
b)
x2 + 6x = 7
Part XII – Factoring by GCF
a)
4y2 + 108y
Part XIII – Solving by Factoring
a)
3x2 – 2x – 8 = 0
(
)(
(
)=0
x=
(first, move 7 over!)
)=0
(
)=0
x=
Part XIV – Solving by GCF
a)
50x2 – 200x = 0
______(
)=0
_______ = 0
(
x=
x=
8x2 - 56x = 0
b)
______(
)=0
_______ = 0
x=
)=0
(
)=0
x=
Part XV – Solve by Taking the Square Root
Solve each quadratic equation by taking the square root of both sides. Simplify all radicals if possible.
DON’T FORGET THE + !!!!
a)
5x2 – 100 = 0
b)
5x2 – 3 = 157
c)
(x – 2)2 + 6 = 42
d)
(x + 4)2 + 14 = 2
Part XVI – Solve by Using the Quadratic Formula
c) x2 – 2x – 30 = 0
x=
-b ± b 2 - 4ac
b) 2 x 2 + 4 x - 4 = 0
2a
Part XVII – Synthetic Division
1. Fully factor 2x3 + x2 – 13x + 6 knowing that (x + 3) is a factor:
2. Divide x4 – 3x2 – 4 by x + 2