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Accuplacer
Elementary
Algebra Review

Hennepin Technical College

Placement Testing for Success

Page 1

Overview
The Elementary Algebra section of ACCUPLACER contains 12 multiple choice Algebra
questions that are similar to material seen in a Pre-Algebra or Algebra I pre-college course
...
On other
questions, solving the problem using scratch paper may be necessary
...




Operations with algebraic expressions that can be simplified using formulas and
expressions, adding and subtracting monomials and polynomials, multiplying and dividing
monomials and polynomials, simplifying with positive rational roots and exponents,
simplifying algebraic fractions, and factoring algebraic expressions
...

Testing Tips

 Use resources provided such as scratch paper or the calculator to solve the problem
...

 Start the solving process by writing down the formula or mathematic rule associated with
solving the particular problem
...

 Make an educated guess if you are unsure of the answer
...
For specific practice exercises using
these concepts, please utilize the resources listed at the end of this guide
...
Simplify: 3 7

2

Grouping Symbols
Exponents
Multiply & Divide (Left  Right)
Add & Subtract (Left  Right)

2
...
Simplify:
(4  5) 2

Scientific Notation
When writing a large number in
scientific notation, the exponent will
be positive
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1
...
00000000000523 in scientific notation
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Write 6
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





3
...
Write final answer in scientific notation
...
Divide

...

3  10 4

Hennepin Technical College

Placement Testing for Success

Page 3

Evaluate Expressions
Find the value of each expression when x = 3, y = – 4, and z = 2
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Evaluate: xyz – 4z

2
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Solve for x :

2
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1
...
Solve for x :

PV = nRT

y = hx + 4x

Word Problems
1
...
The sum of the numbers is 35
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2
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The burgers cost $2
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85 each
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10
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Solve and graph: 2x – 7 > 3
2
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

 

1
...


24 x 4  32 x 3  16 x 2
8x 2

3
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Factor: x2 + 5x – 6

2
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Factor: 4x2 – 36

4
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Solve: 4a2 + 9a + 2 = 0

2
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To multiply or divide: Factor all expressions in numerators and denominators, and
then divide out common factors
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4
3a
 2
1
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Divide: 2
x  2x  8
4  x2

Placement Testing for Success

Page 5

Graphing
Graph each equation on the coordinate axis
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3x – 2y = 6
2
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y = 2
4
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This point is the solution to the system and satisfies both
equations
...

1
...


2 x  3 y  4
y  2 x  4

Radicals
Perform the indicated operations
...
All variables represent
positive numbers
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 8  10 

 12   15 


3
...
2 18  5 32  7 162

4
...
3 7

2

4 2  52
3
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3 + 2(5) – | –7 | = 6

= 147

Scientific Notation
1
...
00000000000523 = 5
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6
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3  103 5  10 6

4
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5  1010

6  10 9
= 2  105
4
3  10

Evaluate Expressions
1
...


5(3)  2
13

(3)(4)
12

Linear Equations in One Variable
1
...
50 – x – (3x + 2) = 0  x = 12

Formulas
1
...
y = hx + 4x 

y
x
h4

Placement Testing for Success

Page 7

Answers (continued)
Word Problems
1
...
” Remember, sum means to add
...
”
2
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To get the total amount of
money spent, multiply the number of items by the cost of the item
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05x = the total dollars
spent on burgers and 0
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The equation is: 2
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85 (14 – x) = 19
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Solving the equation, x = 6
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Inequalities
Solve inequalities the same as equations with one exception
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1
...
3(x – 4) – (x + 1) < –12



x<

1
2

=

8x 2  x  2

Exponents & Polynomials



 

1
...


24 x 4  32 x 3  16 x 2
=
8x 2



3x 2  4 x  2

3
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x2 + 5x – 6 = (x + 6)(x – 1)

2
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4x2 – 36 = 4(x + 3)(x – 3)

4
...


4a2 + 9a + 2 = 0  (4a + 1)(a + 2) = 0  a =

1
and a = –2
4

2
...


4
3a
4a  6a
4(a)
4
10a
5
3a(2)
3a
 2


=
=
=
=
=
2a  2 a  a 2(a  1) a(a  1) 2a(a  1) 2a(a  1)
2a(a  1)
2a(a  1) (a  1)

2
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3x – 2y = 6  y 

3
3
x  3 (slope is and y-intercept is –3)
2
2

2
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y = 2
4
...

1
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2 x  3 y  4
y  2 x  4

Solution: (1, 2)

Radicals
1
...
2 18  5 32  7 162 = 2 9 2  5 16 2  7 81 2 = 6 2  20 2  63 2 = 49 2

 12   15 


3
...


2



 180 


 720  =



 1 1


 4 = 2





3  5 2 3 3  4 2 = 6 9  8 6  15 6  20 4 = 6(3)  7 6  20(2) =  22  7 6

Hennepin Technical College

Placement Testing for Success

Page 10



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