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Intermediate Algebra (MAT12X) Final Exam Practice 1) Solve:
2
2 25x 2
3 2 121x 2
4 64x 9742 x 49125
2 x 47
2x
2) Solve:
1272 xx 049142 xx 1522 xx
121872 xx 22510 xx 03522 xx
3) Solve:
2
246
x 7
632
x
1 1 1
3 15x x
1 1 1
2 18x x
24 5
3
x
3 57 3
4
x
4) Solve:
32 x 4353 x 8 9 5x
373 x 3 2 6 4x 4 5 2x
5) Write the type and number of solutions:
2( ) 2 5f x x x 2( ) 2 1v t t t 2( ) 2 1d f f f
2( ) 4 4c d d d 2( ) 4 1f b b 2( ) 3 2 1g x x x
6) Evaluate the function:
22 7
3
f x x
Evaluate f
2 5
2
f x x x
Evaluate f
2 2
0
f x x x
Evaluate f
2 8
10
f x x
Evaluate f
210 2
4
f x x
Evaluate f
2 7 8
1
f x x x
Evaluate f
7) Determine the smallest set the number belongs to:
49 12 9 16 3625
16 2 4 81 18 64 25
8) Expand and combine like terms:
26 2 3 7x x x 23 2 4x x x 26 8 1 4 6x x x
22 3 2x x x 2 2 1 4 7x x x 22 1 3 3 7x x x
9) Simplify with positive exponents:
2
3 4 2 45 2x y z xy z 2
2 4 2 45 5x y x y
2
5 2 0 5 2 37x y z x y z
3
5 4 3x y z
2
3 2 45x y z
3
4 3 3 2 52x y z x y z
10) Solve the equation for the specified variable:
wl
wforSolve
2250
r
rforSolve
250
yx
xforSolve
6342
rtPE
PforSolve
2gtvts
gforSolve
hrV
hforSolve
2
3
1
3 7x and x 13
33
x and x 4 12x and x
5.22
51 orxandx 1
6
1 xandx 95 xandx
34 xandx rootdoubleortymultiplici
x
2
7 35 xandx
310 xandx rootdoubleortymultiplici
x
2
5 75 xandx
22 xandx 33 xandx 20x
27x 25x 15x
11x 3
44x 2x
34x 35x 21x 2 Real Solutions 1 Real Solution 2 Imaginary Solutions 1 Real Solution 2 Imaginary Solutions 2 Real Solutions
113 f 142 f 00 f
10810 f 224 f 141 f
7 2 3 :Complex Numbersi i 1: Integers 6 5 :Complex Numbersi
0: Whole Numbers 9 3 2 : Irrational Numbers 3: Natural Numbers
422592 23 xxx 3 23 13 6 8x x x 3 224 4 44 6x x x
xxx 672 23 710154 23 xxx 3 26 3 11 7x x x
5 8 920x y z 425
1
yx 15 6 349x y z
12
15 9
y
x z
6
4 825
x
y z 15 11 88x y z
lw 25
25r yx 214
rt
EP
2t
vtsg
2
3
r
Vh
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
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