2013 Final Exam Review- Precalculus Semester 2
1.
Simplify:
a.
(5-3i)2
b. (7 + 6i)(6 + 3i)
2.
Perform the indicated operation:
a. (4 – 3i)(4 + 3i) – (3 +2i)(5 -4i)
b. (2 + i)2 – (3 – i)2
3.
4.
5.
Divide:
a.
5−3𝑖
b.
6+4𝑖
3+2𝑖
2−5𝑖
Find the vertex of the parabola: y = 2x2 – 12x + 22
Using the leading coefficient and end behavior state what happens to the graph of:
a. f(x) = 3x3 + 2x2 – 5x
b. f(x) = -6x6 + 3x5 -2x2 + 4
6.
Which graph represents the function f(x) = x4 -9x2
#7 – 8 Graph the following equations:
7.
f(x) = 2x3 + 3x2 – 8x + 3
8.
9.
f(x) = x3 – 4x2 + x + 6
What is the degree of the polynomial:
a. f(x) = x(x+4)(x-5)(x2 -1)(x3+1)
b. f(x) = (x2-3)(x+1)(x3+ x2 -3x + 2)
10.
Find the zeros of the polynomial.
a. f(x) = x3 – 2x2 + 3x – 2 given that 3 is one of the zeros.
b. f(x) = x4 -3x2 -4 given that -2 is one of the zeros.
11.
Write a polynomial function in standard form of minimum degree with real
coefficients whose zeros include those listed.
a. The zeros are: 3 and 1 + 2i
b. The zeros are: 0, 1, -3
12.
Find all horizontal and vertical asymptotes:
a. 𝑓(𝑥) =
𝑥 2 −4𝑥−32
𝑥 2 −1
V.A. :______________
b. 𝑓(𝑥) =
H.A. :_______________
𝑥+ 9
𝑥 2 + 5𝑥+2
V.A. :______________
H.A. :_______________
For #13 – 16, evaluate each expression.
13.
log 6 1
14.
log 4 4
15.
6log6 15
16.
17.
18.
log10
Write the equation in its equivalent exponential form: log4 x = 5
Write an equation in its equivalent exponential form: .
log5 x = 3
19.
Write the equation in its equivalent logarithmic form: 6x = 1296
20.
Write an equation in its equivalent logarithmic form: 9x = 728
21.
Use Properties of Logarithms to expand the logarithmic function as much as possible.
Wherever possible, evaluate.
log4 x4 √y
22.
Use Properties of Logarithms to write the expression as a single logarithm whose
coefficient
is 1.
5 ln x –
23.
1
ln y
3
3(10-2x) = 81
24.
nt
 r
For #25 – 27, use the compound interest formulas A  P 1   and A  Pert to solve.
 n
25. Find the accumulated value of an investment of $15,000 at 12% compounded annually for 7
years.
26.
Find the accumulated value of an investment of $1810 at 5% compounded quarterly for 19
years.
27.
Find the accumulated value of an investment of $4000 at 7% compounded continuously for
5 years.
28.
Determine the 25th term of the arithmetic sequence: 5, 2, -1, -4, …
29.
Find the sum of the arithmetic sequence: 15, 21, 27, 33, … , 249
30.
Find an explicit rule for the nth term of the geometric sequence: 4, -8, 16, -32, …
31.
32.
33.
34.
Find a10 of the geometric sequence when a1  1000, r 
1
.
2
Evaluate
Evaluate:
Evaluate:
a] 4!
B] (5!) (2!)
35. In a student government election, 6 seniors, 3 juniors, and 2 sophomores are running for
election. Students elect four at-large senators. In how many ways can this be done?
36. How many 4-letter codes can be formed using the letters A, B, C, D, E, and F? No letter
can be used more than once.
37. A hamburger shop sells hamburgers with cheese, relish, lettuce, tomato, onion, mustard, or
ketchup. How many different hamburgers can be concocted using any 5 of the extras?
38. Lisa has 4 skirts, 7 blouses, and 4 jackets. How many 3-piece outfits can she put together
assuming any piece goes with any other?
39. A lottery game has balls numbered 1 through 19. What is the probability of selecting an
even numbered ball or an 11?
40. Two six-sided dice are rolled. What is the probability that the sum of the two numbers on
the dice will be a four?