Math Final

Exam Precalculus Final Exam (Fall 2016)

Name___________________________________

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

Determine whether the given function is one-to-one. If it is one-to-one, find a formula for the inverse. 1) f(x) = 2x2 + 6, x 0 1)

A) f-1(x) = 2

x - 6 B) Not one-to-one

C) f-1(x) = 2

x - 6 D) f-1(x) =

x - 6 2

Find the amount that will be in an account, given the stated conditions. 2) P = $12,000, t = 3, r = 9% compounded quarterly 2)

A) $15,540.35 B) $15,672.60 C) $3672.6 D) $15,327.73

Solve the exponential equation. 3) 3(1 + 2x) = 243 3)

A) 6 B) 2 C) -2 D) 81

Solve the logarithmic equation. 4) log3(2x - 2) = 1 4)

A) 3 B) log31 + 2

2 C)

5 2

D) 5 3

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. 5)

25 15

20

Find sin A and tan A.

5)

A) sin A = 4 5

; tan A = 4 3

B) sin A = 4 3

; tan A = 5 4

C) sin A = 5 4

; tan A = 4 5

D) sin A = 3 5

; tan A = 4 3

Find the requested function value of .

6) If csc = 3 2

, find cot . 6)

A) 5

2 B)

2 5

C) 3 5

D) 5

3

1

Solve the right triangle for all missing sides and angles to the nearest tenth. 7)

c = 28.5 B = 39.5°

7)

A) A = 50.5°, a = 22, b = 18.1 B) A = 50.5°, a = 34.6, b = 44.8 C) A = 50.5°, a = 44.8, b = 36.9 D) A = 50.5°, a = 36.9, b = 44.8

Solve. 8) From a boat on the lake, the angle of elevation to the top of a cliff is 24°50'. If the base of the cliff is

2700 feet from the boat, how high is the cliff (to the nearest foot)?

24°50'

2700 ft

8)

A) 1259 ft B) 1249 ft C) 1262 ft D) 1252 ft

Find the trigonometric function value for the angle shown. 9) sin 9)

A) sin = - 3 4

B) sin = - 3 5

C) sin = 4 5

D) sin = 5 4

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle.

10) 2 3

10)

A) 4 3

; - 8 3

B) 5 3

; - 4 3

C) 5 3

; - 5 3

D) 8 3

; - 4 3

2

Convert to radian measure. Leave your answer in terms of . 11) 165° 11)

A) 10 11

B) 11 12

C) 12 13

D) 5 6

Find the amplitude, period or phase shift.

12) Find the amplitude of y = 4 cos 2x + 2

. 12)

A) 4 B) 2 C) 8 D) 2

Multiply and simplify. 13) sec x (cot x + sin x) 13)

A) cos2x + 2 sin2x B) csc x + tan x C) sin x + csc x D) cos2x - cot x

Factor and simplify. 14) sec x csc x - 5 csc2 x 14)

A) sec x(sec x - 5 csc x) B) (csc x - 5)(sec x + csc x) C) csc x(sec x - 5 csc x) D) csc x(sec x - 5 csc2 x)

Use the sum and difference identities to evaluate exactly. 15) sin 15° 15)

A) - 2( 3 + 1)

4 B)

2( 3 - 1) 4

C) - 2( 3 - 1)

4 D)

2( 3 + 1) 4

Find the exact value.

16) Given that sin = - 4 5

with in quadrant IV, find sin 2 . 16)

A) - 24 25

B) 24 25

C) - 7 25

D) 7 25

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

Prove the identity. 17) tan x + cot x = sec x csc x 17)

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

Find the exact value in radians.

18) cos-1 2

2 18)

A) 11

6 B)

4 C)

6 D)

4

3

Evaluate.

19) cos-1 cos - 6

19)

A) 7 6

B) - 6

C) 6

D) 5 6

Convert to degree measure. Round to two decimal places, if necessary.

20) 5 2

20)

A) 450° B) 72 ° C) 900° D) 144°

4