John Jay College of Criminal Justice/CUNY
MAT 141 Precalculus
Final Exam Review
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer. 5 points
1) log 4 (x + 3) + log 4 (x - 3) = 2
1)
A) {-5}
B) {6}
C) {5}
D) {5, -5}
Solve the equation on the interval [0, 2 ). 5points
2) sin2 x - cos2 x = 0
A)
3
5
7
,
,
4 4
4
4
,
B)
,
4 6
2)
C)
,
4 3
D)
4
Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for a n to find
a 20, the 20th term of the sequence. 5 points
3) 11, 4 , -3, -10, . . .
A) a n = 7n - 18; a 20 = 122
C) a n = 11 - 7n; a 20 = -129
3)
B) a n = 7n - 11; a 20 = 129
D) a n = 18 - 7n; a 20 = -122
Graph the function. (5 points)
4) f(x) = -x + 3 if x < 2
2x - 3 if x 2
A)
4)
B)
1
C)
D)
Express the product as a sum or difference. 5 points
5) sin 8x cos 4x
1
A) (sin 12x + cos 4x)
2
C)
1
(cos 12x - cos 4x)
2
Graph the rational function.
i: Find X and Y intercepts
ii: Find the Vertical and Horizontal Assymptotes
6) f(x) =
4x
x 2 - 36
5)
B) sin (cos 32x 2 )
D)
1
(sin 12x + sin 4x)
2
(10 points )
6)
2
A)
B)
C)
D)
Solve the equation by expressing each side as a power of the same base and then equating exponents. 5 points
7) 8 (x - 6)/6 = 8
7)
A) 8
B) {9}
C) {18}
D) {12}
Find the exact value of the trigonometric function. Do not use a calculator.
9
8) sec 4
A)
2
B)
2
2
C) - 2
8)
2
2
D) -
Use the given information to find the exact value of the trigonometric function. 5 points
1
9) sin = , tan > 0
Find cos .
4
2
A)
8 + 2 15
4
B)
8 - 2 15
4
Express as a single logarithm.
10) ( log a x - log a y) + 2 log a z
xz 2
2xz
A) log a
B) log a
y
y
C)
6
4
D)
9)
10
4
(2.5 points)
10)
x
C) log a
z2y
D) log a xz 2 y
3
Use the vertex and intercepts to sketch the graph of the quadratic function. 2.5 points
11) f(x) = 1 - (x - 1) 2
A)
B)
C)
D)
11)
4
Find the inverse of the one-to-one function. 5 points
5
12) f(x) =
7x - 8
7x - 8
A) f -1 (x) =
5
C) f -1 (x) =
12)
5
8
+
B) f -1 (x) =
7y 7
5
8
+
7x 7
8
5
D) f -1 (x) = - 7
7x
Complete the following:
(a) Use the Leading Coefficient Test to determine the graph's end behavior.
(b) Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis and turns around at each
intercept.
(c) Find the y-intercept.
(d) Graph the function.
10 points
13) f(x) = x 2 (x + 2)
13)
Polar coordinates of a point are given. Find the rectangular coordinates of the point. 5 points
2
14) 9,
3
A) -
9 -9 3
,
2
2
B)
9 -9 3
,
2
2
C) -
9 9 3
,
2 2
D)
9 9 3
,
2 2
Use the given information to find the exact value of the expression. 5 points
4
15) sin = ,
lies in quadrant I
Find cos 2 .
5
A)
7
25
B) -
8
25
C) -
7
25
14)
15)
D)
24
25
5
Match the equation to the graph. 5 points
16) (x + 1) 2 = 7(y - 1)
16)
A)
B)
C)
D)
Verify the identity. 5 ponts
17) csc u - sin u = cos u cot u
17)
Use the formula for the sum of the first n terms of a geometric sequence to solve. 5 points
18) Find the sum of the first 13 terms of the geometric sequence: 7, -14, 28, -56, 112, . . . .
A) 19,117
B) 19,124
C) 19,115
D) 19,111
18)
Find a rational zero of the polynomial function and use it to find all the zeros of the function. 5 points
19) f(x) = x 3 + 6x 2 - x - 6
A) {1, 2, -3}
B) {1, -1, 6}
C) {1, -1, -6}
D) {-1, 2, 3}
The rectangular coordinates of a point are given. Find polar coordinates of the point. Express
5 points
20) (2 3, 2)
A) 4,
3
B) 2,
3
C) 2,
6
19)
D) 4,
in radians.
20)
6
6