Q. Find 𝑓 −1 (𝑥) given 𝑓(𝑥) = 4𝑥 − 3
A. 𝑓 −1 (𝑥) =
𝑥+3
4
2
Q. Find 𝑓 −1 (𝑥) given 𝑓(𝑥) = + 5
𝑥
A. 𝑓 −1 (𝑥) =
2
Q. Expand log 6 (36𝑥 3 )
Q. Convert 15° to radians
A. 2 + 3 log 6 𝑥
A.
√𝑥
64
Q. Expand log 4 ( )
2
2
Q. Find 𝑓 −1 (𝑥) given 𝑓(𝑥) = 𝑥 − 2
3
3
3
𝑥
Q. Expand ln √
𝑒
A. 𝑓 −1 (𝑥) = 𝑥 + 3
A. ln 𝑥 −
Q. Given 𝑓(𝑥) = 𝑥 2 + 3, 𝑔(𝑥) = 4𝑥 − 1,
find (𝑓 ∘ 𝑔)(𝑥)
Q. Solve 125𝑥 = 25 for 𝑥
2
1
3
3
A. 𝑥 =
A. 16𝑥 2 − 8𝑥 + 4
Q. Given 𝑓(𝑥) = √𝑥, 𝑔(𝑥) = 𝑥 + 1, find
(𝑓 ∘ 𝑔)(𝑥)
2
Q. Given 𝑓(𝑥) = √𝑥 − 1, 𝑔(𝑥) = 𝑥 + 3,
find (𝑓 ∘ 𝑔)(𝑥)
A. √𝑥 + 2
Q. Evaluate log 5
1
25
(without a calculator)
Q. Solve 9 𝑥+2 = 27−𝑥 for 𝑥
Q. Evaluate log16 4 (without a calculator)
4
5
Q. Evaluate ln
A. −4
𝑒
4 (without a calculator)
A.
4
Q. Convert
5𝜋
3
(without
3
Q. Determine the amplitude, period, and
phase shift of 𝑦 = 2 sin(𝑥 − 𝜋)
to degrees
A. Amplitude = 2, Period = 2𝜋, Phase
Shift = 𝜋
Q. Convert
7𝜋
5
Q. Determine the amplitude, period, and
3
𝜋
phase shift of 𝑦 = cos (2𝑥 + )
to degrees
3
2
4
A. Amplitude = , Period = 𝜋, Phase Shift
A. 252°
=−
5𝜋
6
𝜋
2
8
Q. Determine the amplitude, period, and
𝜋
phase shift of 𝑦 = −3 sin ( 𝑥 − 3𝜋)
3
A. Amplitude = 3, Period = 6, Phase Shift
=9
Q. Find the reference angle for 265°
Q. Solve log 3 (𝑥 − 1) − log 3 (𝑥 + 2) = 2
for 𝑥
22𝜋
√3
2
A. −
Q. Solve 3 + 4 ln(2𝑥) = 15 for 𝑥
2
(without
7𝜋
A. 150°
𝑒3
6
√3
2
Q. Find the exact value of sin
a calculator)
A. 𝑥 = ln 3
A. No Solution
1
9
Q. Convert 315° to radians
A.
11𝜋
7𝜋
Q. Convert
1
2
Q. Find the exact value of cos
a calculator)
Q. Solve 𝑒 2𝑥 − 𝑒 𝑥 − 6 = 0 for 𝑥
A. 𝑥 =
A. −2
A. −√3
A. 300°
3
A. 𝑥 = −
A. √𝑥 + 1
A.
1
𝜋
12
Q. Convert 140° to radians
A.
1
A. log 4 𝑥 − 3
𝑥−5
Q. Find the exact value of tan 120°
(without a calculator)
to degrees
1
A. 85°
A.
Q. Find the reference angle for −410°
A. 50°
Q. Solve log 4 (2𝑥 + 1) = log 4 (𝑥 − 3) +
log 4 (𝑥 + 5) for 𝑥
Q. Find the reference angle for −
A. 𝑥 = 4
A.
Q. Find the exact value of cos−1 (− )
2
(without a calculator)
3
3
Q. Find the exact value of tan−1 1 (without
a calculator)
A.
11𝜋
2𝜋
𝜋
4
Q. Find the exact value of sin−1 (−
(without a calculator)
𝜋
3
A. −
𝜋
3
√3
)
2
1
Q. Find the exact value of tan [sin−1 (− )]
2
(without a calculator)
Q. Solve sin 3𝑥 = 1 for 0 ≤ 𝑥 < 2𝜋
Q. If 𝐯 = 𝐢 − 5𝐣 and 𝐰 = −2𝐢 + 7𝐣,
evaluate 6v − 3w
𝜋 5𝜋 9𝜋
A. −
A. ,
1
6
6
,
A. 12i − 51j
6
√3
1
Q. Find the exact value of csc [tan−1 ( )]
(without a calculator)
√3
Q. Solve tan 𝑥 = 2 cos 𝑥 tan 𝑥 for
0 ≤ 𝑥 < 2𝜋
𝜋
5𝜋
3
3
A. 0, , 𝜋,
A. 2
Q. Find the exact value of
4
tan [cos−1 (− )] (without a calculator)
A. 15i − 57j
Q. Solve cos 2𝑥 − sin 𝑥 = 1 for 0 ≤ 𝑥 < 2𝜋
5
A. −
A. 0, 𝜋,
3
A.
√6−√2
4
Q. Find the exact value of sin(75°)
A.
√6+√2
4
Q. Find the exact value of cos(105°)
A.
√2−√6
4
Q. Find the exact value of sin 22.5°
A.
√2−√2
2
Q. Find the exact value of cos 22.5°
A.
√2+√2
2
2−√2
A. √
6
,
A. −10i + 41j
6
2+√2
Q. Solve the triangle with 𝐴 = 70°, 𝐵 =
55°, and 𝑎 = 12
Q. If 𝐯 = 2𝐢 + 3𝐣 and 𝐰 = 7𝐢 − 3𝐣, evaluate
𝐯⋅𝐰
A. 𝐶 = 55°, 𝑏 ≈ 10.5, and 𝑐 ≈ 10.5
A. 5
Q. Solve the triangle with 𝐵 = 66°, 𝑎 = 17,
and 𝑐 = 12
Q. If 𝐯 = 2𝐢 + 4𝐣 and 𝐰 = 6𝐢 − 11𝐣,
evaluate 𝐯 ⋅ 𝐰
A. 𝑏 ≈ 16.3, 𝐴 ≈ 72°, and 𝐶 ≈ 42°
A. −32
Q. Solve the triangle with 𝑎 = 26.1, 𝑏 =
40, and 𝑐 = 36.5
Q. If 𝐯 = 2𝐢 + 𝐣 and 𝐰 = 𝐢 − 𝐣, evaluate
𝐯⋅𝐰
A. 𝐴 ≈ 39°, 𝐵 ≈ 78°, and 𝐶 ≈ 63°
A. 1
Q. Use DeMoivre’s Theorem to evaluate
[2(cos 20° + 𝑖 sin 20°)]3 . Write your
answer in rectangular form.
Q. Write the first four terms of the
𝑛+2
sequence 𝑎𝑛 = (−1)𝑛
A. 4 + 4𝑖√3
A. − , , − ,
Q. Use DeMoivre’s Theorem to evaluate
1
𝜋
𝜋
7
=
√2
2+√2
=
2−√2
√2
𝑛+1
3 4
5 6
2 3
4 5
Q. Write the first four terms of the
(−1)𝑛+1
[ (cos + 𝑖 sin )] . Write your answer
2
14
14
in rectangular form.
1
A.
𝑖
sequence 𝑎𝑛 =
Q. Use DeMoivre’s Theorem to evaluate
(−2 − 2𝑖)5 . Write your answer in
rectangular form.
Q. Write the first four terms of the
1
sequence 𝑎𝑛 = (𝑛−1)!
A. 128 + 128𝑖
A. 1, 1, ,
128
Q. Find the exact value of tan 22.5°
Q. If 𝐯 = 𝐢 − 5𝐣 and 𝐰 = −2𝐢 + 7𝐣,
evaluate 3w − 4v
7𝜋 11𝜋
4
Q. Find the exact value of cos(75°)
Q. If 𝐯 = 𝐢 − 5𝐣 and 𝐰 = −2𝐢 + 7𝐣,
evaluate 3v − 6w
1
1 1
1
2
4 8
16
A. , − , , −
1 1
2 6
2𝑛