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Math253
Practice Exam #01
1. The sum of two numbers is 91. One of the numbers is nine more than the other. What are the two
numbers? Set up an equation using x to represent the unknown, solve it, and answer the question.
2.
x + 3 , evaluate the following.
Given f ( x ) =
5 x − 6 and g ( x ) =
2
a)
f ( −2 ) + g ( 0 )
b)
f ( 3)
g ( −11)
3.
Solve the following equations for x.
a)
x 4
− =2 + x
2 3
b)
4
3
(1 − x=
)
( 2 x + 3)
3
4
4. Simplify each expression and write your final answer with only positive exponents.
 x −2 y 3 
a)  5 
 z 
−2
 2 x3 y −2 
b) 
−3 
 3y 
3
5. Find the equation of the that is perpendicular to the line
( 0, − 78 )
4x + 7 y =
1 and has a y-intercept of
. Write your final answer in slope-intercept form.
6. Solve the system using any method.
3x + 4 y − 3z =
4
5x − y + 2 z =
3
x + 2y − z =
−2
7. Quick Copy recently charged $0.49 per page for color copies and $0.09 per page for black-andwhite copies. If Tony’s bill for 90 copies was $12.90, how many copies of each type were made?
8. In triangle ABC, the measure of angle B is twice the measure of angle A. The measure of angle C is
80o more than that of angle A. Find the measure of each angle.
Note: Remember that the interior angles of a triangle sum to 180o.
9. Solve the Inequality and write your answer in Interval Notation.
a) 2 ( 4 + 2 x ) − 20 ≥ 2 x + 3 ( 2 − 5 x )
b)
1
1
( 6 x + 24 ) − 20 > − (12 x + 72 )
3
4
11. Solve the Absolute Value Inequality and write your answer in Interval Notation.
a) 3 x + 4 + 2 ≤ 7
b)
3a + 1 7
≥
5
8
Math253
Exam #01 Solution
Fall 2016
1.
The length of a copper wire 120 cm long is two be cut into two pieces. One of the pieces is threefifths as long as the other. What is the length of each piece? Set up an equation using x to represent
the unknown, solve it, and answer the question.
2. Given f  x   5 x 2  x and g  x   3  x , evaluate the following.
2
a)
f  2   g  3
b)
f  3
g  9 
3.
Solve the following equations for x.
a)
3 x
  3  2x
4 5
b)
3
x
2
(1  )  ( 2 x  3)
4
3
3
4. Simplify each expression and write your final answer with only positive exponents.
 x3 y 2 
a)  5 
 z 
2
 2 x 3 y 5 
b) 

2
 3y

4
5. Find the equation of the line that is perpendicular to the line

2 x  3 y   4 and has a

y-intercept of 0,  4 . Write your final answer in slope-intercept form.
5
6. Solve the system using any method. Be sure to show your work.
2x  3y  z  5
x  3 y  8 z  22
3x  y  2 z  12
7. Two cars travel in the same direction and start at the same location. Car 1 travels at
65 mph and
Car 2 travels at 50 mph. How long will it take for the two cars to be 345 miles apart? Complete the
table and set up an equation to solve this problem.
Rate
Time
Distance
Car 1
Car 2
8. The sum of three numbers is 440. The first number is twice the second number. The first number is
also three times the third number. Find the numbers.
9. Solve the Inequality and write your answer in Interval Notation.
a) 14   3  2 x   2  x  5  x
b)
1
1
 4 x  5  15    3x  6 
3
2
11. Solve the Absolute Value Inequality and write your answer in Interval Notation.
a)
1  4x

3
2

1
4
b) 3x  4  5  12