MAT 150 College Algebra
Spring 2015 Midterm
NAME:_________________
1. Find the midpoint between the two points  3,4 and 5,6 .
2. Perform the indicated additions, subtractions, multiplications, and divisions:
A)

x 3

2

 
B) 2  9  3  4

C)
3
5i
3. Solve the following equation by COMPLETING THE SQUARE: 2 x 2  8 x  6  0
4. Solve the following equation by using the QUADRATIC FORMULA: 4 x 2  4 x  2  0
5. Solve the following equations, do not worry about checking answers and extraneous solutions.
A) 2x  3  3x  4  2x  x  2
B)
C)  2 x  1  9  0
D
2
3
2
1
 2

x x  3x x  3
4
3x  1  5  3
5. Continue to solve the following equations, do not worry about checking answers and extraneous
solutions.
E) x  x  6  0
F) x 6  7 x 3  8  0
6. Solve the following inequalities. To receive full credit, put your final answer in interval notation.
B) x  3  2
A) 3  2 x  5  7
7. Find the x-intercept(s) for the equation
1
2
x y 4
2
3
8. Determine if the equation x 2   y  1  10 is symmetric with the y-axis.
2
9. A graph is shown below. Complete the graph so that it is symmetric with the origin.
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
y
x
1
2
3
4
5
6
7
10. Find an SLOPE-INTERCEPT equation of a line that passes through the points 6,5 and 0,3
11. Graph the three equations below on the grids provided. To receive full credit you must plot at
least THREE points.
y
A) y  3 
7
6
5
4
3
2
1
2
 x  2
3
x
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
y
B)
 x  3   y  2 
2
2
4
7
6
5
4
3
2
1
x
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
C) x 2  y  4
y
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
x
12. Your hourly pay rate varies inversely with the cubed root of hours working. If 27 hours of work
gives you an hourly rate of $10, find the constant of proportionality for this situation.
13. Three relations are shown. For each, determine if the relationship is a function. Explain your
reasoning.
y
7
A)
B)
C) x  y  4
6
x
-3
-2
-1
0
1
2
5
4
3
2
1
y
5
4
2
2
4
5
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
x
1
2
3
4
5
6
7
14. Find the domain for each function that you see below:
7
6
5
4
3
2
1
A)
y
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
B) f ( x) 
x 5
x  x6
2
C) g ( x)  3x  5
x
1
2
3
4
5
6
7
EXTRA CREDIT –
A) Solve:
x  4  x  5 1
B) Find the equation of a circle whose center is at 3,4 and that has an x-intercept at  2,0
Enjoy your Spring Break!!
MAT 150 College Algebra
Spring 2015 Midterm Calculator Version
NAME:_________________
Calculator Type:_________
Use your calculator to do the following problems on this part of the quiz.
1. Estimate the following values. Round your answer to 3 decimal places.
A) x 
8  3 17
5
B) x 
5
8  3 17
C) x 
5  3 17
8  3 17
2. Solve the equation x3  3x  4  0 . Estimate the solution(s) to 3 decimal places.
2. Solve the equation x3  2 x  7  0 . Estimate the solution(s) to 3 decimal places.
2. Solve the equation x 2  2 x  7  0 . Estimate the solution(s) to 3 decimal places.
3. Solve the equation x 2  2 x  x  3 . Estimate the solution(s) to 3 decimal places.
3. Solve the equation 3x  x 2  x  4 . Estimate the solution(s) to 3 decimal places.
3. Solve the equation
x  1  3  4  x . Estimate the solution(s) to 3 decimal places.
4. Solve the inequality x  2 
1
x  4 . Put your final answer in interval notation.
2
1
16
4. Solve the inequality  x   x  4 . Put your final answer in interval notation.
3
3
4. Solve the inequality 1  x  x  4 . Put your final answer in interval notation.
5. Graph the equation x   y  3  5
2
5. Graph the equation  y  3  x  5
2
5. Graph the equation x   y  5  3  0
2