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