Math 125 Practice Test #1 (Chapter 3 to Chapter 5)
1.
Perform the indicated operations and simplify each expression.
Write your answers using positive exponents.
(a)  42  40
 x 2 y 4 y 3 
(d) 

5
 x

2.
3.
4.
(b)
 7 x y  4x y 
(e)
(4k 5 )0
(2k ) 3
3
2
3
3
2
 2k 2 m 4 
 4 7 
 k m 
(c) (2 x 4 y 3 ) 4
2
Find the product and simplify each expression.
(a) (5n  3m) 2
(b) 4 y 3 (2 y  5)( y  3)
Divide.
5a3b 2  15ab4  20ab6
(a)
5ab 2
(b)
6x
2

 13x  8   x  1
Factor each expression completely.
(a) 6n 4  24n 2
(b) 2 x 2  x  5
(d) x 2  9 xy  36 y 2
(e) 27 x 3  64
(g) x 4  14 x 2  32
(h) x3  2 x 2  36 x  72
(j) 8m3  125n3
(c) (a  2b)3
(c) (3x 3  12 x  4)  ( x  2)
(c) 9 y 2  6 y  1
(f) 36 x3 y  24 x 2 y 2  45 xy 3
(i) 81x 4  625 y 4
5.
Perform the indicated operations and express your answers in simplest form.
x3  1
x2 1
18  8n2
6n 2  7 n  3
(a)
(b)


x2  x  2 2x  4
2n2  5n  3 n 2  9n  8
10
2
8
3

(c)
(d)
 2
2
2
2
x  5x x
x  10 xy  25 y
x  4 xy  5 y 2
2x  2
x 1
 2
(e)
2
x  4 x  3 x  5x  6
6.
Simplify the complex fraction and express your answers in simplest form.
3
5
3

1
a 2  4
2x 3 y
x

3
(a)
(b)
(c)
2
4 3
2  a 1
1

x2
x 4y
7.
What are the values for which the given expression is undefined?
x3  8
x2  8x
8.
Solve each equation.
(a) 4n3  36n
2
y
(c)
3
y2
y2
(b)
x  2x  7  18
(d)
2
2t  3
6t  5

 2
t  3 t  1 t  2t  3
9.
Solve the given formulas for the indicated variable.
x y
1 1 1
  1 for y
 
(a)
(b)
for S
a b
R S T
10.
For the following word problems, you must set up an equation and solve to
earn full credit. No guessing please!
(a)
The reciprocal of a number equals the reciprocal of the difference of 4
and the number. Find the number.
(b)
A rectangle is twice as long as it is wide. Its area is 98 square meters.
Find the length and the width of the rectangle.
(c)
The product of two consecutive room numbers is 110. Find the room
numbers.
(d)
In a right triangle, the length of one leg is 3 cm less than the other leg.
If the length of the hypotenuse is 15 cm, find the lengths of the two legs.
(e)
Bob rides his bicycle 30 miles in the same time that it takes Larry to ride
his bicycle 20 miles. If Bob rides 5 miles per hour faster than Larry, find
the rate of each.
(f)
If Jerry can paint a room in 5 hours and Annie can paint it in 10 hours,
how long would it take them to paint the room together?
__________________________________________________________________________
Answer key is on the next page.
Answer Key for Math 125 Practice Test #1 (Chapter 3 to Chapter 5)
1.
(b) 112x y
(a) 17
(d)
8
y3
x9
x16
(c)
16 y12
5
(e) 2k 15 m6
2.
(a) 25n 2  30mn  9m 2
(b) 8 y 5  4 y 4  60 y 3
3.
(a) a 2  3b 2  4b 4
(b) 6 x  7 
4.
(a) 6n2 (n  2)(n  2)
(b) not factorable or prime (c)
(d)
(g)
(j)
5.
(a)
1
x 1
(c) a 3  6a 2b  12ab 2  8b 3
(c) 3 x 2  6 x  24 
(e)  3x  4   9 x 2  12 x  16  (f)
 x  12 y  x  3 y 
 x2  2   x  4  x  4  (h)  x  2 x  6 x  6 (i)
 2m  5n   4m2  10mn  25n 2 


2 x2  x  1
(b) 
 x  1 x  1
(c)
2
x5
(e)
x 1
 x  1 x  2
2  9 y  10 x 
(d)
 x  5y  x  y
2
x2
x3
(c) 
7.
The rational expression is undefined when x  0 or x  8 .
8.
(a)
3,0,3
(c) no solution
(b)
2
3n  1
5 x  23 y
(a)
3 16 y  3 x 
(b)
 3 y  1
3xy  2 x  3 y  6 x  5 y 
 9 x2  25 y 2  3x  5 y 3x  5 y 
2  n  8
6.
4, 1
 1

(d)  ,  6 
 2

44
x2
1  2a
a
y
bx  ab
a
9.
(a)
10.
(a) The number is 2.
(b)
S
RT
T R
(b) width = 7m; length = 14 m.
(c) The room numbers are 10 and 11.
(d) 12 cm and 9 cm
(e) Larry's rate is 10 mph; Bob's rate is 15 mph.
(f) 3
1
hr or 3 hr 20 min
3