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)