Pre-Calculus
2nd Semester Final Review 2022
chapters 4,5, 6, 7, 8, 10
Name___________________________________
SHORT ANSWER. Write the word or phrase that best
completes each statement or answers the question.
Use the Pythagorean Theorem to find the length of the
missing side.Then find the indicated trigonometric
function of the given angle. Give an exact answer with a
rational denominator.
Convert the angle in degrees to radians. Express answer as
a multiple of π.
4) Find sin θ.
1) - 54°
10
3
Find the exact value of the indicated trigonometric
function of θ.
15
2) tan θ = , 270°< θ < 360°
Find cos θ.
8
Use the given triangles to evaluate the expression. Rationalize
all denominators.
Find the reference angle for the given angle.
3) -388°
5) sin
1
π
π
π
csc + tan
4
4
3
Find the exact value of the expression.
7π 5π
6) cos
12 12
Solve the triangle. Round lengths to the nearest tenth and
angle measures to the nearest degree.
Solve the equation on the interval [0, 2π).
Use the given vectors to find the specified scalar.
10) a = 8, b = 14, c = 16
7) sin2 x + sin x = 0
11) u = 12i + 8j and v = 12i - 9j; Find u ∙ v.
Use substitution to determine whether the given x-value
is a solution of the equation.
-3π
8) cos 2x = - 2, x =
4
Let x represent one number and let y represent the other
number. Use the given conditions to write a system of
nonlinear equations. Solve the system and find the
numbers.
12) The sum of two numbers is -8 and their
product is 12. Find the numbers.
Write the complex number in rectangular form.
2π
2π
9) 5(cos
)
+ i sin
3
3
Solve the system of equations.
13) x - y + 4z = 14
4x
+ z=3
x + 5y + z = -7
2
Evaluate the determinant.
14)
Solve the problem.
17)
59
-2 6
1
Let A = -3
2
and B =
-1
3 . Find A - 4B.
-2
Find the inverse of the matrix, if possible.
15)
A = -2 -3
-3 0
Use the formula for the general term (the nth term) of a
geometric sequence to find the indicated term of the
sequence with the given first term, a 1 , and common ratio,
r.
18) Find a 11 when a 1 = 5, r = -3.
Solve the matrix equation for X.
16)
2 -2
Let A = 1 -7
4 -4
-1 -1
and B = -8 -8 ;
6 -2
Write a formula for the general term (the nth term) of the
arithmetic sequence. Then use the formula for a n to find
X-B=A
a 20, the 20th term of the sequence.
19) 15, 11 , 7, 3, . . .
Write the first four terms of the sequence whose general
term is given.
20) a n = 4(n + 2)!
3
Answer Key
Testname: 2ND SEMESTER FINAL REVIEW
1) -
3π
radians
10
17)
ID: PCALC7Z 4.1.4-4
2)
8
17
ID: PCALC7Z 8.3.4-4
18) 295,245
ID: PCALC7Z 4.4.2-8
ID: PCALC7Z 10.3.3-5+
3) 28°
4)
ID: PCALC7Z 4.4.3-4
19) a n = 19 - 4n; a 20 = -61
3
10
20) 24, 96, 480, 2,880
ID: PCALC7Z 10.2.3-8
ID: PCALC7Z 10.1.3-3
ID: PCALC7Z 4.3.1-7
5) 1 +
3
ID: PCALC7Z 4.3.2-10
3
2
6)
ID: PCALC7Z 5.2.1-2
7) 0, π,
3π
2
ID: PCALC7Z 5.5.3-8
8) No
ID: PCALC7Z 5.5.1-4
9) -
5 5 3
i
+
2
2
ID: PCALC7Z 6.5.4-5+
10) A = 30°, B = 61°, C = 89°
ID: PCALC7Z 6.2.1-8
11) 72
ID: PCALC7Z 6.7.1-2
12) -6 and -2
ID: PCALC7Z 7.4.4-1
13) {(0, -2, 3)}
ID: PCALC7Z 7.2.2-2
14) 48
ID: PCALC7Z 8.5.1-2
15)
-
0-
1
3
1
3
2
9
ID: PCALC7Z 8.4.1-15
16)
5
-15
10
1 -3
-7 -15
10 -6
ID: PCALC7Z 8.3.5-3
4