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Math 1050 Final Exam - Fall Semester 2004 Form A
Name___________________________________ Instructor__________________________________
Student ID: _____________________________ ID Verification: ____ Class Time: ________________________________
This exam has three parts. Part I - Ten multiple choice questions Part II - Ten open ended problems - you MUST show all your work. Part III - Choose FIVE out of ten open eneded problems - you MUST show all your work. This exam is closed book and closed notes.
Determine whether the relation represents a function. If it is a function, state the domain and range.
- {(- 1 , 8 ), ( 1 , 5 ), ( 5 , - 5 ), ( 7 , - 1 )} A) function domain: {-1, 1, 5, 7} range: {8, 5, - 5, - 1}
B) function domain: {8, 5, (^) - 5, (^) - 1} range: {-1, 1, 5, 7}
C) not a function
Determine whether the sequence is geometric.
- 4, 12, 36, 108, 324, ... A) geometric B) not geometric
Find an equation for the line with the given properties.
- Perpendicular to the line y = - 3 x + 3 ; containing the point (- 2 , 3 ) A) y = 1 3
x + 11 3
B) y = 3x + 11 3
C) y = - 1 3
x + 11 3
D) y = - 3x + 11 3
Express as a single logarithm.
- 3 log 6 x + 5 log 6 (x - 6)
A) log 6 x(x - 6)^15 B) 15 log 6 x(x - 6) C) log 6 x^3 (x - 6)^5 D) log 6 x(x - 6)
Find the center (h, k) and radius r of the circle with the given equation.
- x^2 + y^2 + 12x - 10y = - 52 A) (h, k) = (- 5 , 6 ); r = 9 B) (h, k) = ( 5 , - 6 ); r = 3 C) (h, k) = ( 6 , - 5 ); r = 9 D) (h, k) = (- 6 , 5 ); r = 3
Form a polynomial f(x) with real coefficients having the given degree and zeros.
- Degree: 3; zeros: - 2 and 3 + i. A) f(x) = x^3 - 8x^2 + 2x + 20 B) f(x) = x^3 - 4x^2 - 10x + 20
C) f(x) = x^3 - 4x^2 - 2x + 20 D) f(x) = x^3 - 6x^2 - 10x + 20
Find the indicated term for the sequence.
- an = 2 n - 2 ; a (^15)
A) 32 B) 28 C) 0 D) 30
Part Two Questions 11-20: Short Answer Answer all TEN questions. You must show all your work in a clear logical progression to receive full credit.
Complete the following:
- a) Determine the domain of log 3 (x (^) - 24)
b) Determine the domain of log3 (x )
c) Find all the real solutions of log3 x + log3(x - 24) = 4
Find the real solutions of the equation.
- x + x = 90
Graph the function.
f(x) = - x^ +^2 x^ <^0 x + 3 x ≥ 0
-5 5 x
y
-5 5 x
y
Solve the system using the either inverse matrix method or Gaussian elimination.
x + 2y + 3z = 4 x (^) + y (^) + z (^) = 2
The inverse of
is
-^3 5
Find the sum of the infinite geometric series.
∞
k= 1
k- 1
Given the ellipse find the center, foci, and vertices of the ellipse. Then Graph the ellipse.
- 2x^2 + 3y^2 - 16x + 36y + 134 = 0
Center: _________________
Foci:____________________
Vertices: ________________
-5 -4^ -3^ -2^ -1^1 2 3 4 5 x
5 y 4 3 2 1
-5 -4^ -3^ -2^ -1^1 2 3 4 5 x
5 y 4 3 2 1
Complete the following steps.
- a) Use the Factor Theorem to show (x - 5) is a factor of f(x) = x^4 - 21x^2 - 100.
b) Use synthetic division and the Rational Roots Theorem to determine all the remaining rational zeros of f(x).
c) Factor f(x) completely over the real numbers.
Answer the following questions given the function:
- f(x) = 3 x^ -^1 x - 1
a) Is the point (0,-1) on the graph?
b) If x=2, what is f(x)?
c) What is the domain of f(x)?
Find the sum of the sequence.
5
k = 1
∑ (k^ -^ 4)
Solve the inequality.
- (x^ -^ 3)
x2^ - 36
Solve the problem.
- A local civic theater has 22 seats in the first row and 21 rows in all. Each successive row contains 3 additional seats. How many seats are in the civic theater?
Write the partial fraction decomposition of the rational expression.
- x^ -^3 (x - 5)(x - 4)
Solve the equation.
- 3 2x^ + 3 x^ - 6 = 0
Solve the problem.
- A right triangle has one vertex on the graph of y = x^2 at (x, y), another at the origin, and the third on the (positive) y-axis at (0, y). Express the area A of the triangle as a function of x.
Answer Key
Testname: 1050 FINAL A
1) A
2) A
3) A
4) C
5) D
6) C
7) B
8) D
9) A
10) A
- x (^) = 27
- { 81 }
-5 5 x
y 5
-5 5 x
y 5
- x = - 7 , y = 16 , z = - 7
- A(x) = - x^2 + 500x; {x|0 < x < 500}
- f - 1(x) (^) = 5x^ +^2 3 - x
; domain of f: {x x (^) ≠ - 5}; range of f: {y y (^) ≠ 3}
12
(x^ -^ 4)
center: (4, (^) - 6); foci: (5, (^) - 6), (3, (^) - 6); vertices: (5.7, (^) - 6), (2.3, (^) - 6)
- Yes
- function
- 3
- 23.129 years
- odd
- (-∞, - 6 ) or ( 6 , ∞)
- 1092 seats
- 2 x - 5
+ -^1
x - 4
x = ln 2 ln 3
A(x) = 1 2
x
Answer Key
Testname: 1050 FINAL A
-10 -5^5 10 x
y 10
5
-10 -5^5 10 x
y 10
5
domain: (-∞, ∞) range: (-1, ∞) horizontal asymptote: y = - 1
