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ALGEBRA 2 NAME: ___________________________
CHAPTER 3 TEST Review PER: ___________ Complete all work in your MATH NOTEBOOK! You may use a graphing calculator to solve problems #19-20, 29-30 only! Solve by factoring.
1. x^2 6 x 16 0
Solutions: ___________________________
2. 10 x x^2 24
Solutions: ___________________________
Solve by square rooting.
3. x^2^ 49 85
Solutions: ___________________________
4. (3 x 1)^2 1 25
Solutions: ___________________________
Solve by completing the square.
5. x^2^ 7 6 x
Solutions: ___________________________
6. 4 x^2 8 x 12 0
Solutions: ___________________________
Solve using the quadratic formula. Solutions may contain complex numbers.
7. ^ x^2^^ ^5 x^2
Solutions: ___________________________
8. 3 y^2 12 y 13 0
Solutions: ___________________________
Determine the number and type of roots for the quadratic shown. 9.
Number of roots: ________ Type of roots: _________________
Number of roots: ________ Type of roots: _________________
Number of roots: ________ Type of roots: _________________
Simplify. Write each as a complex number in standard form.
12. ^2 ^3 i^^ ^7 ^6 i 13.^9 ^3 i^ ^ ^2 ^7 i 14.^5 ^6 i^ ^4 ^7 i 15. 15 33 16. 5 121 20 17.^^ i^99
X (^) 2,4 8 4 2 X 12
X 6 4 6
X (^1) 326,4 (^326)
4 3 52 4 3 E^ X^ Hir^ X^ I^ if
X (^5) 17,
(^5) F 2 2
X (^6) 353,4 6353
2 I^2 Real Real^ imaginarycomplex
5 31 11 101 62 111
355 11 315 I
18. Fill in the missing steps to derive the quadratic formula. 1. ax^2 bx c 0 2. __________________ 3. __________________
2 2 2
x b^ x b^ c^ b
a a a a
5. __________________
2 2
x b^ ac^ b
a a
§ ·^ ^
7. __________________
x b^ b^ ac
a a
r^
9. __________________
19. Use a calculator to solve by graphing. Round solutions to the nearest 10 th^.
y 0.14 x^2 3.2 x 10
Solutions: _____________________________
20. Use a calculator to solve the system by graphing. Round solutions to nearest 10th. 2 2
y x x
y x x
Solutions: _____________________________
Solve each system using substitution. 21. 2
y x x y
Solutions(s): _____________________________
22.^2
x x y y x
Solutions(s): _____________________________ Solve each system using elimination. 23.^2 2
x x y x x y
Solutions(s): _____________________________
24.^2 6
x x y y x
Solutions(s): _____________________________ Graph the inequalities.
25. y t x^2 6 x 8 26. y x^2 8 x (^16) 27.^2 2
4 2 ( 2) 4
y x x y x
t
28.^2
2
2 2 4
y x y x x
! d
29. A rectangular playground must have a perimeter of 320 meters and an area of at least 5000 square meters. Find the possible lengths, rounded to the nearest whole number, of the playground.
Possible lengths: ___________________________
30. The equation p ( x ) = – 0.3 x^2 + 400 x – 21000 represents the profit p (in dollars) for x games produced at EA Sports. Find the number of games the company must produce to earn a profit of at least $30,000.
Number of games: ___________________
xu baxt^ g O yabax^ Ea
x (^) La eatbar
my
XtLa^ beggar
10.4 1 7 and 1 1.2^ 2.
1 9 41 and^ 4,241 14,23^ and^1 1
13.1 14,
r a^ r^ a
I Isolation T purple
YoItionim^
r
The possible^ lengths are between^ 43m and 117m
The (^) company must produce at least (^143) games
By Quadratic^ Formula (^7) X21. 2 8 342 124 13 0 42 5 2 0 y
bIVb2 Hac X Za bIVb2 Hac Za 4 112 51,272^4137113 x 5 IV52 411712 21 1 4 12111464 156 51135 8 4
12 IF X (^5117) 4 121, X (^57117) 4 65
IF x (^5 117) X (^5 ) y 6 V3^ y 6 YV
(^9 11) on (^) graphs
1271 2 311 17 61 13 19 31 1 2 74 14 15641 4 71 2 7 31 61 9 31 2 71 20 351 241 4212 5 31 9 2 31 72 20 111 4211 11 101 20 42 111 62 111
15 FS (^) F3 17 199 its.ir
16155 Mtf if 11 zits ftp.iz.i I'T (^1) zig
(^124) tl i
355 in
18 19 4 0.14^2 3.2 10
X 3 7 19.
(^20 4 3 2 5 ) 4 43 2
1 1.22.77^8 r 10.4.1.7 and 1 1.2^ 2.
By substitution (^21 4 5 )
40 I
22 2 2 5 1
IIIa 2 2 4 53 54
0 42 5 36 2 2 6 8 0 21 2 3 47 0 0 1 9 X 4 21 411 17 0
X 9 9 44 44
yea
K 4
4 4 x 4 Y
When (^) x (^9) when (^4) EFFI's 4 5 4 4 5 4 4 5191 4 4 5141 4 When^4 4 When^ X^1 4 45 4 4
5 3 4 5 3 4 4 Y^24
4 4 5141 3 4 5111 3 I 4 20 3
YI
1 9 41 and (^) 4,24 4 23 d 14,23 and^1 1
(^29) P 320M (^30) pix 0.3 2 400 21000 A at least^5000 x profitat least 30000 A 25000 PIX^230000 length X P 2142W^ A l^ W PIX^ 0.3^2 400 320 300001 0.3^2 400 (^2 24 50001) XY (^160 4 4 50001 1160) x O^ E^ 0.^
(^2 400 )
4 160 X^50001160 X^ X OE X (^160 5000) Call Findzeros car Findzeros if (^) Y 4 142.79^4 1190. i 4 42.58^4 117.42^1431 (^431 1117) The (^) company must produce at least (^143) games The possible (^) lengths are between^ 43m and 117m
