Math 1050 Section 1 Final
Name:
Read all directions carefully and show all your work for full credit. Each question
is worth 5 points for a total of 100 points.
Good Luck!!!
1. Solve the following system of equations using Gaussian Elimination, GaussJordan Elimination, or Crammer’s Rule.

 x − 3y + z = 4
2x − 7y + 2z = 7

−3x + 9y − 4z = −11
2. Find all solutions to the equation
|x − 1| = 4.
4. Sketch the graph of the function f (x) =
−(x − 3)2 + 2 below.
3. Find an equation for the line passing through the points (-2,3) and
(5,6).
5. If h(x) = x3 − 4x + 1 and g(x) =
x2 − 2 then find (h ◦ g)(x).
6. Find the coordinates of the vertex
of the parabola −3x2 + 12x − 5.
8. Sketch the graph of the function (x+
4)2 (x−2)(x+1)2 using the x-intercepts.
9. Perform the division
7. Factor the following polynomial completely 2x3 − 9x2 + 4x + 15.
x3 − 4x2 + 2x − 1
x−2
10. Condense the following to a logarithm of a single quantity.
12. Sketch the graph of the function G(x) =
log2 (x).
1
5log2 (x + 3) − log2 (2x − 1) + log2 5
3
2
11. Find all solutions to 34x 32x = 3−3x+6 .
13. Find the determinant
2 7 −1
3 0 −9
−4 1 0
14. Find g(2) where g(x) = 4x4 − 9x3 +
6x2 − 10x + 9
15. Perform the following matrix multiplication


−4 1
2 −1 3
· 2 7 
0 5 −7
−1 3
16. Write out the first 5 terms of the
sequence an = (−1)n 2(n − 1).
17. Find
P4
n=1 (2
+ 3n−1 ).
18. Simplify (4 − 2i)2 . (IE write as a
complex number of the form a + bi
where a, b in R)
19. Expand (3x + 2)4 using Pascal’s triangle.
20. Jill has a job that pays $4 on the
first day. Every subsequent day she
gets paid 3 dollars more than she
did the previous day. For example
on day 2 she gets $7 and on day
three she gets $10 and so on. How
much does Jill make in 100 days?
To answer this question you should
use one of the formulas below.
1 − rn
n
Sn = (a1 +an ) or Sn = a1
2
1−r