1 FINAL EXAM TOPIC ASSIGNMENT There are 50 questions altogether. 32 questions on the non-calculator section & 18 questions on the calculator section. TOPIC With Calculator Non- Calculator Trigonometry Transformations Parametric Equations Summation Notation Binomial Expansion/Specific Term Sequence/Series Exponential Graphs Exponential/ Banking Applications Solving Exponential Equations Properties of Logs Log Graphing Solving Log Equations Polynomial Function and Graphs Zeros of Polynomials Rational Functions and Graphs The above chart is subject to slight modification. A calculator may be used for questions indicated with an “*”; do all other questions by hand – no calculator!.
29
Embed
TOPIC With Non- Calculatorsites.tenafly.k12.nj.us/~jwestervelt/PreCalc/SpringExamReview{2014}.pdf · Log Graphing Solving Log Equations Polynomial Function and Graphs Zeros of Polynomials
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
1
FINAL EXAM TOPIC ASSIGNMENT
There are 50 questions altogether.
32 questions on the non-calculator section &
18 questions on the calculator section.
TOPIC With
Calculator
Non-
Calculator
Trigonometry
Transformations
Parametric Equations
Summation Notation
Binomial Expansion/Specific Term
Sequence/Series
Exponential Graphs
Exponential/ Banking Applications
Solving Exponential Equations
Properties of Logs
Log Graphing
Solving Log Equations
Polynomial Function and Graphs
Zeros of Polynomials
Rational Functions and Graphs
The above chart is subject to slight modification.
A calculator may be used for questions indicated with an “*”;
do all other questions by hand – no calculator!.
2
Review for Spring Exam 2014
For questions 1 and 2, consider the pair of parametric equations: 4
2 3
x t
y t
______1. Find the rectangular form of the parametric equations above.
(A) 22 5y x
(B) 22 11y x
(C) 5
2
yx
______2. Find the restrictions placed on t, x, and y.
(A) 4, 0, 5t x y
(B) 4, 0, 5t x y
(C) 4, 0, 5t x y
______3. Identify the curve for the pair of parametric equations: cosθ
cos2θ
x
y
(A) parabola opening up
(B) a portion of a parabola opening up
(C) vertically-oriented hyperbola
(D) a portion of a vertically-oriented hyperbola
______4. Which graph best illustrates the parametric equations 2sinθ 1
3cosθ 1
x
y
(A) (B) (C)
x
y
x
y
x
y
3
______5. Identify the curve for the parametric equations: 2 23 , 1 2x t y t
(A) (B) (C) (D)
______6. Evaluate 77
8
3n
(A) 207
(B) 210
(C) 231
______7. Evaluate 5
0
!
2n
n
(A) 77
(B) 77.5
(C) 154
______8. Find the sum: 6
2
1 2k
k
k
(A) 40
(B) -4
(C) 6
(D) 8
x
y
x
y
x
y
x
y
4
______9*. 400!
398! 2!=
(A) impossible
(B) 79,800
(C) 159,600
______10. ( 1)!
( 1)!
n n
n
=
(A) 2n n
(B) 2
1
n n
(C) 1
1n
______11. 2 !
(2 3)!
n
n=
(A) 2
2 3
n
n
(B)
2
1 2n n
(C) 2 1 2n n n
(D) 2 2 1 2 2n n n
______12. Which of the following is the definition of e?
(A) 1
2
!n
n
n
(B) 1
1
!n n
(C) 0
1
!n n
5
______13*. Evaluate: 16
14
(A) 8/7
(B) 120
(C) 224
______14. Which of the following is not equal to 1 if x is any whole number?
(A) x xC
(B) 0xC
(C) 1xC
______15. Find a value of x (other than 50) for which the following is true: 500 500
50 x
(A) 450
(B) 250
(C) 10
______16. Expand 4
5 2i without a calculator.
(A) –41–840i
(B) 41 +840i
(C) 41–840i
______17*. Find the middle term in the expansion of
10
2
4
xy
.
(A)
510263
256
x y
(B) 5 5252x y
(C) 5 1063
256
x y
6
______18. Find the term containing x6 in the expansion of
83x y .
(A) 6 228x y
(B) 5 628x y
(C) 6 628x y
(D) 6 256x y
______19. Use the Binomial Theorem to expand 3
2 .x y
(A) 3 2 2 32 6 6x x y xy y
(B) 3 2 2 38 4 2x x y xy y
(C) 3 2 2 32 3 3x x y xy y
(D) 3 2 2 38 12 6x x y xy y
______20*. Given the explicit definition, find the 30th
term: ( 1) 2
4 5
n
n
na
n
.
(A) 12
25
(B) 12
23
(C) 12
23
______21. Find the tenth term of the sequence whose nth term is defined as
2 1
5 3 1n
na
n
(A) 21
32
(B) 21
72
(C) 22
32
(D) 19
29
7
______22. Which of the following is the recursive definition for the sequence shown below?
1
120, 40, 13 ,...3
nd
(A)
11
1203
n
nd
(B) 1 1
1120,
3n nd d d
(C) 1
1
3n nd d
(D) 1 1120, 3n nd d d
______23. Which of the following is an arithmetic sequence?
(A) 2, 4, 8, 16, 32,... (B) 2, 4, 8, 16, 32,...
(C) 3, 6, 9, 12, 15,... (D) 2, 4, 6, 10, 16,...
______24. In an arithmetic sequence, 5 38a and 9 21a . Which is the 25th
term in the sequence?
(A) –47
(B) 165.5
(C) –17.75
______25. Which of the following is a geometric sequence?
(A) 1 1 1 1
2, , , , ,...2 4 6 8
(B) 2, 4, 8, 16, 32,...
(C) 2, 0, 2, 4, 6,... (D) 2, 7, 3, 8, 4,...
______26*. In a geometric sequence, 2 80000g and 6 32768g . Which is the 7th
term in the sequence?
(A) 100000
(B) 26214.4
(C) 20971.52
(D) 16777.216
______27. Rewrite the following definition explicitly: 1 n n-1A 9, A 4 A
(A) n 1nA 9(4) (B) nA 9 4n (C)
n 1
n
1A 9
4
(D) nA 5 4n
8
______28*. Find the sum of the finite arithmetic sequence: 5,9.5,14,...,68}
(A) 543
(B) 547.5
(C) 552
(D) 556.5
______29*. Find the sum: 500
1
3 5n
n
(A) 756, 500
(B) 376,250
(C) 752,500
(D) 378,250
______30*. Find the sum of the finite geometric sequence: 1,3,9,...,6561
(A) 9841
(B) 11327
(C) 18336
(D) 29524
______31*. Find the sum of the expression: 10
0
32
5
n
n
to four decimal places.
(A) 4.9698
(B) 5.0000
(C) 4.9819
(D) 55.0000
______32*. Determine whether the infinite geometric series converges and if so, find the sum:
500 100 20 4 ...
(A) diverges (B) converges; 624
(C) converges; 625 (D) converges; 626
9
______33*. Evaluate: 0
25
3
n
n
(A) 6
(B) 3
(C) 1
(D) 0
______34. Solve for x:
2 1
5127
9
x
x
(A) x = 4/3
(B) x = –17
(C) x = 13/7
_____35*. The population of Bedrock is 14,500. If it decreases at a rate of 2½ % per year, what will the
population be in 10 years?
(A) 816.55
(B) 1462.31
(C) 11256.78
(D) 18561.22
_____36*. The population of Smallville is 50,000. It increases at a rate of 3.12% per year. In how many
years will it reach 60,500?
(A) 0.16 years
(B) 0.7 years
(C) 4.5 years
(D) 6.2 years
10
_____37*. A substance weighing 10 grams has a half-life of 36 days. After how many days will the
substance weigh only 2 grams?
(A) 63.14 days
(B) 75.68 days
(C) 83.59 days
(D) 92.34 days
_____38. Which of the following is the graph of 24 3xy ?
(A) (B) (C)
For questions 39-42, match each function with the correct graph.
______39. 14 3xy (A) (B) (C)
______40. 34 3xy
______41. 22 4 3xy (D) (E)
______42. 24 1xy
______43. Which of the following is the graph of 1 1xy e ?
(A) (B) (C)
(3, -2)
(-1, -4)
(2, 0)
(-2, -1)
(1, -4)
x
y
(2, -2)
x
y
(-2, -2)
x
y
(-2, -2)
x
y
(1, 2)
x
y
(-1, 2)
x
y
(-1, -2)
11
______44. The domain of 3 xy e is:
(A) 3, (B) 0, (C) , (D) ,3
______45. The range of 3 xy e is:
(A) ,3 (B) ,3 (C) 3, (D) ,
_____46. Determine the x-intercept: 22 3 5xy
(A) 3log 2.5 2
(B) ln2.5 2ln3
ln3
(C) 2.5log 3 2
(D) 2log3 log2.5
log3
_____47. Which of the following is not equivalent to 21(2) 2
2
xy ?
(A) 21(2) 2
2
xy
(B) ( 2)1(2) 2
2
xy
(C)
21 1
22 2
x
y
(D)
21 1
22 2
x
y
(E) ( 2)1
2 22
xy
_____48*. Determine how much money must be deposited at 9% interest compounded monthly in order to
have a balance of $35,000 after 20 years.
(A) $5824.45
(B) $6914.23
(C) $9470.02
(D) $12500.00
12
_____49*. If $9200 is invested at 9.5% interest compounded continuously, find the balance in the account
after 10 years.
(A) $17940.00
(B) $22628.35
(C) $23788.53
(D) $25040.56
For questions 50-53, match each function with one of the graphs shown on the right.
_________50. 1
2 3x
y
(A) (B)
_________51.
11
32
x
y
_________52. 212 3
xy
(C) (D)
_________53.
211
2 32
x
y
__________54. Identify the CP’ for
21
5 42
x
y
(A) (-2, 4)
(B) (-2, -1)
(C) (-2, 9)
__________55. Which functions have a point that is a “cusp” at the CP’?
(A) x
y b (B) 2xy b
__________56. Which functions have a smooth, rounded shape at the CP’?