Practice Problems for MTH 65 Proficiency Test
Set A
Remember that you may not use books, notes or calculators on the proficiency test. The
following problems are practice for the various types of problems that might appear on
the test.
Solve for the variable in the following equations:
1. 2x 32 6 2. 4x 23.8 5
3. 3a 2 5a 8 4. 2 ( x 3) –5
2
5. 2 3(t 3) 3(t 11) 6. x24
3
1 1 5 4
7. a a
2 3 6 3
Solve the following inequalities for the variable and graph the solution set:
8. x 2x 4 9. 2( x 3) 3x 2
Spring 11
Find the slope and the y-intercept of the following equations:
10. y – 4x 2 11. 3 y 4x 5
Write the following equations in slope-intercept form:
12. 3x y –2 13. x 3 y 10
Find the slope of the line that passes through each pair of points below:
14. (–2, –1), (–4, –5) 15. (–1, –2), (–5, –2)
Given the slope and y-intercept of the line below, sketch the graph of the line:
4
16. slope ; y-intercept = –1
3
Spring 11
Write an equation of the line that passes through the given point and has the given slope.
Write your answer in slope-intercept form.
3
17. slope = – ; (–8, –1)
4
Write an equation for each of the lines sketched below. Each square on the graph
represents one unit.
18. 19.
20. Make a table of values that includes at least three points, and sketch the graph:
y – 4x 1
x y
Spring 11
Answers to Proficiency Practice Problems – Set A
1. x 13 2. x 4.7 3. a5
11
4. x 10 5. t 6. x 3
3
7. a5 8. x4
0 4
9. x 4 10. Slope: -4, y-intercept: (0, 2)
)
-4 0
4 5
11. slope: , y-intercept: 0, 12. y 3x 2
3 3
1 10
13. y x 14. Slope is 2
3 3
y
15. Slope is 0 16.
3
17. y x7
4 1
1 x
18. y x 1
2
1
19. y x 1
3
y
20.
x y
–2 9
–1 5
0 1 1
1 -3 x
2 -7
Spring 11