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Math 1111 Final Practice Fall 2007
Name: Last ____________________. First ____________________
You must show your work and/or provide explanations for your answers for all questions.
Otherwise, no credit will be given.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find an equation for the line with the given properties.
- Parallel to the line 2 x
9 y
24 ; containing the point ( 3 ,
A) 3 x
9 y
24 B) 2 x
9 y = -
48 C) 2 x
9 y = -
48 D) 9 x
2 y = -
Perform the indicated operations and simplify the result. Leave the answer in factored form.
x
x
A)
14 x - 18
x(3 - x)
B)
14 x - 18
x(x - 3)
C)
18 x - 14
x(x - 3)
D)
18 x - 14
x(3 - x)
Find the real solutions, if any, of the equation. Use the quadratic formula.
- 8x
x
A) {
} B) {
C) {
} D) no real solution
Solve the equation.
- 9 x - 18 = 3 x - 48
A) {- 5 } B) {- 8 } C) { 8 } D) { 5 }
Find the vertex and axis of symmetry of the graph of the function.
- f(x) = -
7x
14x
A) (
17 ) ; x = -
2 B) ( 1 ,
24 ) ; x
C) ( 2 ,
59 ) ; x
2 D) (
1 , 4 ) ; x = -
For the given functions f and g, find the requested function and state its domain.
- f(x) = 16 - x
; g(x) = 4 - x
Find f + g anf (f + g) (-2)
A) (f + g)(x) = 4 + x; {x|x ≠ - 4}, (f + g) (-2) = 2
B) (f + g)(x) = - x
- x + 20; all real numbers, (f + g) (-2) = 18
C) (f + g)(x) = - x
- x + 12; all real numbers, (f + g) (-2) = 6
D) (f + g)(x) = x
- 16x + 64; all real numbers, (f + g) (-2) = 72
Find the quotient and the remainder.
- 16x
- 21x + 15 divided by 4x + 1
A) 4x
- 5x - 4; remainder 19 B) 4x
C) x
Form a polynomial whose zeros and degree are given.
- Zeros: - 3 , - 2 , 2 ; degree 3
A) f(x) = x
- 4x + 12 for a = 1 B) f(x) = x
C) f(x) = x
- 4x + 12 for a = 1 D) f(x) = x
- Zeros: 0, - 6 , 5 ; degree 3
A) f(x) = x
- 30x for a = 1 B) f(x) = x
C) f(x) = x
- 30x for a = 1 D) f(x) = x
The function f is one
to
one. Find its inverse.
- f(x) =
5 x
A) f-1(x) =
x + 3
B) f-1(x) =
x - 3
C) f-1(x) =
x
x
- f(x) = (x + 6)
A) f
1(x)
x - 216 B) f
(x) = x - 6
C) f
1(x)
x - 6 D) f
1(x)
x + 6
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
- Instruments on a satellite measure the amount of power generated by the satellite's power
supply. The time t and the power P can be modeled by the function P = 50e
is in days and P is in watts. How much power will be available after 378 days? Round to
the nearest hundredth.
Solve the equation.
- 2x
A) {6} B) {3} C) { 35 , - 35 } D) {3, - 3}
Change the logarithmic expression to an equivalent expression involving an exponent.
- log
A) 64
= 4 B) 4
= 64 C) 3
= 64 D) 4
Change the exponential expression to an equivalent expression involving a logarithm.
A) log
B)
log
log
4 C) log
D) log
A) log
= 5 B) log
5 = - 2 C) log
= - 2 D) log
Use a calculator to evaluate the expression. Round your answer to three decimal places
log 9 + log 4
ln 3 - ln 8
A) - 0.359 B) - 3.654 C) 0.490 D) - 1.
Solve the problem.
- Find a so that the graph of f(x) =
log
a
x contains the point ( 13 , 16 ).
A)
13 B)
C)
16 D)
- f(x) =
x + 2
and g(x)
.
Find the point of intersection of the graphs of f and g by solving f(x) = g(x).
A) (1, 27 ) B) ( 27 , 1) C) (1, 9 ) D) ( 9 , 1)
- The population of a particular country was 29 million in 1985 ; in 1997 , it was 38 million. The
exponential growth function A =29ekt describes the population of this country t years after 1985.
Use the fact that 12 years after 1985 the population increased by 9 million to find k to three decimal
places.
A) 0.023 B) 0.183 C) 0.033 D) 0.
Use a graphing calculator to solve the equation. Round your answer to two decimal places.
- e
x
= x
A) {-0.71} B) {2.54} C) {-1.15} D) {0}
Find the amount that results from the investment.
- $480 invested at 12 % compounded quarterly after a period of 7 years
A) $618.21 B) $1098.21 C) $1061.13 D) $1066.
Solve the problem.
- Kimberly invested $ 4000 in her savings account for 8 years. When she withdrew it, she had
$5085.00. Interest was compounded continuously. What was the interest rate on the account?
Round to the nearest tenth of a percent.
A) 2.9% B) 3.1% C) 3 % D) 3.15%
- Suppose that $ 4000 is invested at an interest rate of 5.6% per year, compounded continuously. What
is the doubling time?
A) 13.4 yr B) 2 yr C) 12.4 yr D) 11.4 yr
Solve the inequality. Express your answer using interval notation.
- |5x + 2| > 3
A) (
) B) [
]
C) (-∞, - 1] or [
, ∞) D) (-∞, - 1) or (
- In the decimal number system (base 10), what is the value of the ninary number 10101011
A) 171 B) 10,101,011 C) 255 D) 185
Solve the problem.
- A bank loaned out $61,000, part of it at the rate of 15 % per year and the rest at a rate of 7 % per year.
If the interest received was $6430, how much was loaned at 15%?
A) $28,000 B) $27,000 C) $34,000 D) $33,
Find the distance d(P
, P
) between the points P
and P
29) P
= ( 1 , - 3 ); P
A) 14 B) 26 C) 13 D) 169
Answer Key
Testname: MATH1111-FINAL-PRACTICE
1) B
2) B
3) D
4) A
5) D
6) B
7) A
8) D
9) C
10) A
11) C
- 14.18 watts
13) C
14) D
15) B
16) A
17) C
18) D
19) A
20) A
21) A
22) C
23) B
24) C
25) C
26) D
27) A
28) B
29) C
30) D
31) C
