Accuplacer Math Study Guide.

Accuplacer Math Study Guide
The following sample questions are similar to the format and content of questions on the

Accuplacer College Level Math test. Reviewing these samples will give you a good idea of how

the test works and just what mathematical topics you may wish to review before taking the test

itself. Our purposes in providing you with this information are to aid your memory and to help

you do your best.



I. Factoring and expanding polynomials

Factor the following polynomials: Expand the following:

1. 15a3b2  45a2b3  60a2b 9.  x 1 x 1 x  3


2. 7x3 y3  21x2 y2 10x3 y2  30x2 y 2
10.  2 x  3y 


3. 6x4 y4  6x3 y2  8xy2  8 11.  x 3  3   x 6  6 


4. 2x2  7xy  6y2 2
12.  x 2  2x  3

5. y4  y2  6
5
13.  x  1
6. 7x  56 y
3 3




7. 81r4 16s4 6
14.  x  1


2
8.  x  y   2  x  y  1




II. Simplification of Rational Algebraic Expressions

Simplify the following. Assume all variables are larger than zero.
162
1

,1. 32  5  4  40 4. 2 18  5 32  7

2. 9  35
  8  2  27
81
x4 6x 18 12x 16
3. 
5.


3x2  2x  8 4x 12




III. Solving Equations

A. Solving Linear Equations

1. 3  2  x 1  x 10 3. y  y  2  y2  6

x x
2.  1 4. 2  x  1  3x   3  x  1


2 7




B. Solving Quadratic & Polynomial Equations

 8  2 
1. y  y   0 5. t2  t 1  0




  
3 3

  

2. 2x3  4x2  30x  0 6. 3x3  24

3. 27x3  1 2
7.  x  1  x2  25


4.  x  3 x  6  9x  22 8. 5y2  y  1



2

,C. Solving Rational Equations

1. 1  2 11 2 1

y 1
0

y 1
4.  x5
x2  25

x5

2 3 12 1 6
2.   5. 




x3 x3 x2  9 a a2  5

1 2 5x 1 1 x
3.   6.  




6x x3 x2  3x 18 x2  3x x x3




D. Solving Absolute Value
1
Equations 4. x 
1 3
2 4 4
1. 5  2z 1  8

2. x  5  7  2
 5. y 1  7  y

3. 5x 1  2





E. Solving Exponential 1. 10x  1000

Equations


2

, 2 1
4. 3x 9x  


2. 103x5  100 3

x1 1 2 1
3. 2  5. 2x  42x  

8



8
F. Solving Logarithmic Equations

1. log2  x  5  log2 1 5x 4. ln x  ln2x 1  0

2. 2log3  x 1  log3 4
 x 5. ln x  ln x  2  ln 3

3. log2  x 1  log2  x 1  3
6. 32 x  4x1




G. Solving Radical

Equations 4. x2  9  x  1  0

1. 4 2 y 1  2  0


2.2x 1  5 8 5. 3
3x  2  4  6
3.5x 1  2
x 1  0 6. 4 w2  7 2



IV. Solving Inequalities

Solve the following inequalities and express the answer graphically and using interval notation.

A. Solving Linear Inequalities

3 5
1. x  4  2
3