Sample
Diagnostic Test Solutions
After taking the sample form of the diagnostic pretest, check
your answers with the solutions given below. If you have difficulty
with this test, you should obtain a high school algebra book,
or an intermediate or developmental algebra book, determine
what caused you to miss problems that you missed, and practice
additional problems similar to problems that you missed.
1. Express without using any exponents.(2
pts each)
a. (—1)4
a-3 b4
b. 7 x4y0
2. Express using exponential notation.(2
pts each)
a. 2nnnnwww
b. 8•8•xxxzzzzz
or 82
x3z5
c.
3. Combine like terms: (2
pts each)
a. 8a — 4 — 15b
+7 + 14b + 4a  12a —
b + 3
b. y + 3y3+11y2+
9y + 7y3 — 2y2
10
y3+
9 y2 + 10 y
c. 13wx — 11
+ 7xw —
4xw — 4wx — 2
12 wx —
13
4. Carry out operations indicated and simplify:
(3 pts each)
a. 
b. —1
— 4(—
8)
31
c. 3w2(5w4—
3w2)
+ 2 — 7w(w2+3w)
15w6 —
9w4 —
7w3 —
21w2
+ 2
d. 6(7 —
12 ÷ 3) —
5• 3
3
e. 
f. (a —
7)(3a + 1)
3a2 —
20a —
7
5. Evaluate the following expressions if a
= 4and b = -2 (3pts each)
a. 2ab —
b
-14
b. -3ab2 —
(-3a)2 -192
6. Evaluate the following expression if m=0.12,
n=3.01, p=0.024
(3 pts )
nm
+ mp
+ np
0.436
7. Factor out the common factor then write
an equivalent factored expression for the given expression
. (2 pts each)
a. 16xy —
12xz + 2x
2x ( 8y —
6z + 1)
b. 7a2b4c5
+21ab5c3 —
14a3 —
14a3bc2
7a(
ab4c5+
3b5c3 —
2a2 —
2a2bc2)
8. Solve each of the following equations and
check your solutions. (2 pts each)
a.  w=
12 w
= 20
checking
()(20)
= 12
12 = 12
b. 0.7c = 81.4
c = 116.3
checking
0.7(116.3) = 81.4
81.4 = 81.4
c. 5x —
11 = 23
x = 6 =
checking
5() —
11 = 23
34 —
11 = 23
d. 4(7x —
3) = 8 —
4x x
= 
checking
4(7 ( ) —
3) = 8 —
4()
4( 
—  )
= 8 —
=
e. 5(9x —
12) + 25 = 7x x
= 
checking
5(9() —
12) + 25 = 7()
5( —
) + 
= 
=
9. Solve these percentage problems. (3
pts each)
a. Compute 84% of 70.
84% of 70 is 58.8
b. Find w, if 72% of w is 126.
w = 175
10. Consider the equation 
(3 pts each)
a. Express the given equation (above)
in a different form by solving the
given equation for m.
b. Express the given equation (above)
in a different form by solving the
given equation for k. 
11. Express 
in a different form by solving for c . (3
pts)
12. Determine whether the numbers indicated
are solutions to the equations given. Give your answer
by filling in each blank. (2 pts
each)
a. y = 3;
8y — 12
= 7y — 9
y = 3 _is___a
solution.
(is or is not)
b. w = -1;
5w + 3 = 2
w = -1_is
not__a solution.
(is or is not)
13. Specify the domain for each of the given
functions. (2 pts each)
a. 
domain: 
b.
domain: all real numbers
14. Plot the points with these coordinates. LABEL
YOUR POINTS. (1 pt. each)
A (6, 5), B (-3, 4), C (0, -2) D (5, -3),
E (3, 0), F (3.4,  )
15. Give the coordinates of these points. (2
pts each)
A(_2_,_5_),
B(_5_,_-2_),
C(_-5_,_0_)
16. Identify the coordinates of 3 points which
are solutions to y = 3x + 1.
Make a table of values of these coordinates, plot
these points, and sketch the graph of the solutions to the equation
__x __ y__
-2 -5
0 1
2 7
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