Math 1050 Section 1 Final Review
Name:
Read all directions carefully. The review will be graded on completion and will be
worth 30 homework points. You can nd the complete solutions to the review posted
on my website www.math.utah.edu/~malone.
1. Find all solutions to the equation
p
2x + 19 = x + 2
2. Find all solutions to the equation jx2 3xj = 2.
3. Graph all solutions to x4 + 10x 15x2 24 on the real number line.
4. Find all the solutions to the equation
4x + 3 + 2x 1 = 1
x 5 x 3
5. Find an equation for the line passing through the points ( 2; 3) and (7; 4).
6. Find an equation for the line perpendicular to 4x 3y + 7 = 0 passing through
the point (2; 1).
p
x + 2 3.
7. Sketch the graph of the function g(x) =
8. Determine whether or not the set of solutions to the equation (x 3)2 + 4(y +
2)2 = 25 is a function.
9. Name a function with the following graph.
6
5
4
3
-2
2
4
p
6
10. Say f (x) = 7x2+1 and g(x) = x 4 then nd (g+f )(x); (f g)(x); (g=f )(x); (f g)(x); and g f (x)
11. Find the maximum value that f (x) = 4x2 3x + 7 attains.
12. Sketch the graph of the function t(x) = (x 3)2(x + 2)(x 1).
13. Factor the following polynomial completely 6x4 7x3 23x2 + 14x + 24.
14. Perform the division
x4 + 4x3 5x2 + 7x 11
x2 + 1
15. Find f (3) where f (x) = 10x8 31x7 +5x6 +11x5 40x4 40x3 +26x2 16x +4.
16. Sketch the graph of the function
h(x) = x 1 3 + x +1 3
17.
18.
19.
20.
21.
22.
Sketch the graph of the function P (x) = 2x.
Sketch the graph of the function R(x) = log5x.
Find all solutions to 2log5(x) + log5 (x3 25x + 1) = 2.
Find all solutions to 24x2 22x = 1024 2522x
Simplify log3( 91 ) = and log1020.
Write the following as a sum, dierence, and constant multiple of logarithms of
x; y; z.
log6(4x2 y 31 z 4yx )
23. Condense the following expression to a logarithm of a single quantity
4log2(x 1) + 1 log4(x + 1) log8(x2 + 1)
3
24. Solve the following system of equations using Gaussian Elimination, GaussJordan Elimination, or Crammer's Rule.
8 2x + 3y 4z = 8
<
: x3x+ 2y4y z z==2 4
25. Find the partial fraction decomposition for
3x + 17 :
2
x + 2x 15
26. If A; B; C are as below then nd and simplify (if possible) A + B; A B; B A; 4B A 3C; B A C .
0 4 5 1
1 0 6 2 1 1
C
B
2
3
C
B
A = @ 10 21 A ; B = 5 9 5 8 ; and C = 0 1
1 7
27. Find
1 2 4 3 0 2 3 0 5 1 2
2 4 0 9 10 28. Find the area of the triangle with vertices at (1; 2); (0; 4); (6; 1).
29. Determine if the points (3; 2); ( 1; 7); (4; 5) are collinear (lie on the same line).
30. Find the inverse of the following matrix
3 5
1 4
31. Find the rst ve terms of the sequence an = 2(an 1)2 where a1 = 1.
32. Find a formula for the nth term of the sequence 4; 2; 0; 2; 4; 6; 8; : : :.
33. Give an example of a sequence of the following type: a geometric sequence, an
arithmetic sequence, a sequence that is neither arithmetic nor geometric, and a
sequence which is both arithmetic and geometric.
34. Find
8
X
(1 256
k ):
2
k=4
35. Find
1
X
n=3
5( 1=4)n
2
36. You are out looking for a job and stumble across the following opportunities.
The rst is as a manual sewer cleaner in Salt Lake City. This job pays $1 on
the rst day and doubles on every subsequent day for 14 hours of work. IE you
get $2 dollars the second day and $4 dollars the day after that. The second
job is at a video game testing company (3 hour work day) which has a starting
salary of $10,000 dollars a day and gives you a $10,000 raise daily. How much
do you make doing each job for 30 days? How many days extra would you have
to work doing the second job to make more than at the rst job in just 30 days?
37. Expand (2x 5)3 using Pascal's Triangle.
38. Expand ( 3x + y)5 using the Binomial Theorem.
39. If R(x) = x4 2x3 + x 1 then nd and simplify the dierence quotient
R(x h) R(x) ; h 6= 0:
h
40. Simplify (4i 1)(i2 3i + 2) (5i + 6)(2i + 1).