Math C170 FinalExam Practice 52

7/31/2019 Math C170 FinalExam Practice 52

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Review Exercises for Final Exam (Chapters 1- 6, 8- 11)

There are 25 questions on the Final Exam. Please show your work step by step to ge full credit. You may use Calculator anda Formula Sheet , one page bothsided. Formula Sheet could only contains, difinitions, theorem, and reminder ntoes. It must be turn in with your exam. No exeptions.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Find the slope (if defined) of the line that passes through the given points.1) (- 1, 8) and (- 7, - 1) 1)

Determine the intervals on which the function is increasing, decreasing, and constant.2)

x-10 10

y10

-10

x-10 10

y10

-10

2)

Provide an appropriate response.3) Explain how the graph of g(x) = f(x) - 9 is obtained from the graph of y = f(x). 3)

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Fill in each blank with the appropriate response.

4) The graph of y = - 15

- x + 2 can be obtained from the graph of y = x by reflecting across

the __- axis, vertically shrinking by a factor of ___ , reflecting across the __- axis, andshifting vertically ___ units in the _______ direction.

4)

Graph the function.5)

f(x) = 4 if x 1

- 2 - x if x < 1

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

5)

Divide as indicated. Write the quotient in standard form.

6) 7 + 3i

6 - 9i6)

Solve the equation using the zero - product property.

7) x2 + 2x - 15 = 0 7)

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Use synthetic division to decide whether the given number is a zero of the given polynomial.8) - 3; P(x) = - 4x3 + 9x2 + x - 186 8)

What is the domain of f(x)? What is its range?

9) f(x) = - 6x

9)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Match the description with the appropriate rational function.10) The x- intercept is 5.

A) f(x) = x + 5

x + 9B) f(x) = x

- 5x + 9

C) f(x) = 5x - 1

x + 9D) f(x) = x

+ 9x - 5

10)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Find all complex solutions for the equation.11) 5x- 2 - 9x- 1 - 2 = 0 11)

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Use transformations to explain how the graph of the given function can be obtained from the graph of the appropriate

root function (y = x or y =3

x).

12) y = x - 3 + 9 12)

If f is one - to - one, find an equation for its inverse.13) f(x) = 7x - 5 13)

Solve the equation.14) log5

25 = x 14)

Graph the function.15) f(x) = log4

x

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

15)

Graph the parabola.16) y = 3(x - 4)2 + 2

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

16)

Find the length of the arc intercepted by a central angle in a circle of given diameter or radius. Round your answer toas many places as your calculator will allow.

17) Diameter 26.42 ft, = 5.70 radians 17)

Determine the value of the trigonometric function of s using the given information.

18) sin s = 45 , cos s = - 3

5Find tan s. 18)

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Suppose that is in standard position and the given point is on the terminal side of . Give the exact value of theindicated trig function for .

19) (- 2, - 4); Find tan . 19)

Use an appropriate identity to find the exact value of the expression.

20) sin 11

1220)

21) sin (165) 21)

Use the given information to find the exact value.

22) cos A = 13 , 0 < A <

2; sin B = - 1

2 , 3

2 < B < 2 Find cos (A + B). 22)

Decide whether the equation is or is not an identity.23) sin (A + B) sin (A - B) = sin2A - sin2B 23)

Use an

identity

to

write

the

expression

as

a single

trigonometric

function

or

as

a single

number.

24) 2 tan 30

1 - tan 23024)

Identify the equation as either an identity or not.

25) 1 - tan

1 + tan = 1 - sin 2

cos 225)

Use a sum - to - product identity to rewrite the expression.26) sin 8 + sin 26 26)

Solve the equation for solutions in the interval [0, 2 ).27) 8 sin x - 8 = - 4 27)

Solve the equation in the interval [0, 2 ). Express solutions as approximations to the nearest hundredth.28) 6 sin2x - 5 sin x - 1 = 0 28)

Solve the triangle.29)

20 m

29)

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Find the missing parts of the triangle.30) A = 30.0

a = 20.06 b = 40.12

30)

Solve.31) Two tracking stations are on the equator 175 miles apart. A weather balloon is located on a

bearing of N 34E from the western station and on a bearing of N 15E from the easternstation. How far is the balloon from the western station?

31)

Solve the triangle.32) a = 8.10 km, b = 11.49 km, C = 110.3

(Round lengths and angles to the nearest tenth when necessary.)32)

Solve the triangle. Find angles to the nearest hundredth of a degree.33) a = 8.3 in., b = 13.0 in., c = 15.2 in. 33)

Find the indicated vector.34) Let u = 3, - 3 , v = - 1, 4 . Find u + v. 34)

Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round toone decimal place.

35) 35)

Write the vector in the form ai + bj. Round a and b to 3 decimal places if necessary.

36) 9, 5 36)

Solve the problem.37) If u = < - 3, 5 > and v = < 4, - 5 > , evaluate (2u ) v. 37)

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Plot the point, given its polar coordinates.38) (- 4, 210) 38)

Write out the first five terms of the sequence.39) an = 2n - 1 39)

Decide whether the given sequence is finite or infinite.40) 4, 5, 6, 7, ... 40)

Evaluate the sum. Round to the nearest hundredth, if necessary.

41)4

k= 1(4k - 2) 41)

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question).42) The first term is 17, and the common difference is 6; n = 5 42)

Find the sum of the first n terms of the following arithmetic sequence.43) a1 = 1, d = - 2; n = 6. 43)

Evaluate the sum.

44)8

i= 1(i + 6) 44)

Find the indicated term of the geometric sequence.45) a1 = 5, r = 5, n = 3 45)

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth.46) a2 = 12, a5 = 96 46)

Find the common ratio r for the given infinite geometric sequence.47) 2, 6, 18, 54, 162, ... 47)

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Evaluate the expression. Do not use a calculator.

48) 10!7!

48)

Evaluate the expression.

49) 4!2! 2!

49)

Write the binomial expansion of the expression.50) (2x + 3)4 50)

51) (3x + 4)5 51)

Use mathematical induction to prove that the statement is true for every positive integer n.

52) 12 + 42 + 72 + . . . + (3n - 2)2 = n(6n2 - 3n - 1)

252)

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Answer KeyTestname: MATH C170 FINALEXAM PRACTICE (52)

1) 32

2) Increasing on [- 1, ); Decreasing on ( - , - 1]3) Shift the graph of f downward 9 units.

4) y; 15

; x; 2; upward

5)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

6) 539

+ 913

i

7) {- 5, 3}8) Yes9) Domain: ( - , 0) (0, ); range: (- , 0) (0, )

10) B

11) - 5, 12

12) Shift the graph of y = x to the right 3 units andupward 9 units.

13) f- 1(x) = x + 57

14) {2}15)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

16)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

17) 75.297 ft

18) - 43

19) 2

20) 2( 3 - 1)

4

21) 2( 3 - 1)

4

22) 3 + 2 26

23) Not an identity24) 325) Identity26) 2 sin 17.0 cos (- 9.0)

27)

6, 5

628) {1.57, 3.31, 6.12}29) C = 103, a = 9 m, b = 16 m30) B = 90.0, C = 60.0, c = 34.7431) 519 miles32) c = 16.2 km, A = 28, B = 41.733) A = 33.08, B = 58.75, C = 88.1734) 2, 135) 146.5 lb36) 9i + 5j

37)-

74

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Answer KeyTestname: MATH C170 FINALEXAM PRACTICE (52)

38)

39) 1, 3, 5, 7, 940) Infinite41) 3242) 17, 23, 29, 35, 4143) - 2444) 8445) a3 = 12546) a1 = 6, r = 247) 348) 72049) 650) 16x4 + 96x3 + 216x2 + 216x + 8151) 243x5 + 1620x4 + 4320x3 + 5760x2 + 3840x + 1024

52) Answers will vary. One possible proof follows.

a). Let n = 1. Then, 12 = (1)(6(1)2 - 3(1) - 1)

2 = (1)(2)

2= 1. So, the statement is true for n = 1. b). Assume the statement is true for n = k:

Sk = k(6k2 - 3k - 1)

2.

Also, if the statement is true for n = k + 1, thenSk+ 1 = Sk + (3(k + 1) - 2)2 =

(k + 1)(6((k + 1)2 - 3(k+ 1) - 1)2

.

Subtract to get:Sk+ 1 - Sk = (3(k + 1) - 2)2 =

(k + 1)(6((k + 1)2 - 3(k+ 1) - 1)

2 - k(6k2 - 3k - 1)

2Expand both sides and collect like terms:

9k2 + 6k + 1 = 6k3+ 15k2+ 11k+ 2

2 -

6k3- 3k2 - k2

9k2 + 6k + 1 = 18k2+ 12k+ 2

2 = 9k2 + 6k + 1

Since the equality holds, then the statement is true forn = k + 1 as long as it is true for n = k. Furthermore,

the

statement

is

true

for

n =

1.

Therefore,

thestatement is true for all natural numbers n.

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Math C170 FinalExam Practice 52