Math Questions With Answers (2)

A set of multiple choice comprehensive math questions are presented. The questions are related to logarithm, exponential, equations, trigonometry, trigonometric identities, and many other math topics. The answers are provided and are located at the lower part of the page. The questions have been designed to test for deep understanding of math concepts. Solutions and explanations are included.

Question 1

If f(x) = Log(x), then f -1(x) =
A. 10 x
B. -10 -x
C. 1 / 10 x
D. x 10

Question 2

Log 465 =
A. 1.21
B. 1.81
C. 3.06
D. 3.01

Question 3

If 2 3x - 1 = 16, then x =
A. 3/5
B. 5/3
C. 1
D. 4

Question 4

If Log x9 = 2, then x =
A. 2/9
B. 9/2
C. 81
D. 3

Question 5

If x 2 + kx - 6 = (x - 2)(x + 3), then k =
A. 6
B. 3
C. 1
D. 0

Question 6

The vertex of the graph of y = 2x 2 + 8x - 3 is given by
A. (8 , -3)
B. (-2 , -11)
C. (-4 , -11)
D. (-2 , -3)

Question 7

The quadratic equation whose roots are at x = 3 and x = 5 is given by
A. (x - 3)(x - 5) = 1
B. (x + 3)(x + 5) - 9 = (x + 3)(x + 5) - 25
C. (x + 3)(x + 5) = 0
D. x 2 - 8x = -15

Question 8

The roots of the equation x / (x + 2) + 3 / (x - 4) = (4x + 2) / (x 2 - 2x - 8) are
A. x = 4 and x = 1
B. x = 4 only
C. x = 1 only
D. x = -4 only

Question 9

If the domain of function f given by f(x) = -x 2 + 6x is given by the interval [0 , 6], then the range of f is given by the interval
A. [0 , 9]
B. [0 , 6]
C. [0 , 3]
D. [3 , 6]

Question 10

The x intercepts of the graph of y = -x 2 + 3x + 18 are given by
A. (6 , -3)
B. (-3 , 6)
C. (-3 , 0) and (6 , 0)
D. (3 , 0) and (-6 , 0)

Question 11

The domain of f(x) = 2 Log |x - 2| is given by the interval
A. (-infinity , 2) U (2 , + infinity)
B. (-2 , + infinity)
C. (2 , + infinity)
D. (-infinity , + infinity)

Question 12

If 1.56x = 2, then x =
A. ln 1.56 / ln 2
B. ln 2 / ln 1.56
C. 2 / ln 1.56
D. ln 2 / 1.56

Question 13

The reference angle to angle a = -1280o is equal to
A. 20o
B. 30o
C. 160o
D. 60o

Question 14

If x is an angle in standard position with point A(-3 , 4) on the terminal side, then sec(x) =
A. 5 / 3
B. -5 / 3
C. -3 / 5
D. 3 / 5

Question 15

If x is an angle in standard position and it terminal side is in quadrant IV and is given by y = -x, then sin(x) =
A. √ 2
B. 1 / √ 2
C. - √ 2
D. -1 / √ 2

Question 16

Which statement is NOT true?
A. cos(-x) = cos(x)
B. tan(-x) = tan(x)
C. the amplitude of y = -2 cos (t) is equal to 2
D. the range of y = -5 sin (t) is given by [-5 , 5]

Question 17

Which statement is true?
A. sec(-x) = - sec(x)
B. the range of y = tan(x) is given by (0 , + infinity)
C. the period of y = -2 cos (3 Pi t) is equal to 2Pi / 3
D. the period of y = -5 tan (0.5 Pi t) is equal to 2

Question 18

The radian measure of an angle of 25o is equal to
A. 25 Pi
B. 5 / (36 Pi)
C. 5 Pi / 36
D. 36 / (5 Pi)

Question 19

The period of the function f(x) = sin(x Pi/6 + Pi/4) is equal to
A. 2 Pi
B. 12
C. Pi / 6
D. 6 Pi

Question 20

Which of the following is an identity?
A. cos(2x) = 2 cos(x)
B. cos(x + y) = cos(x) + cos(y)
C. sin(x - y) = sin(x) - sin(y)
D. sin(2x) = 2 sin(x) cos(x)

Question 21

Which of the following is NOT an identity?
A. cot(x + y) = [ 1 + cot(x) cot(y) ] / [ cot(x) + cot(y) ]
B. tan(x + y) = [ tan(x) + tan(y) ] / [ 1 - tan(x) tan(y) ]
C. sin(x - y) = sin(x) cos(y) - cos(x) sin(y)
D. cos(2x) = 2 cos 2(x) - 1

Question 22

If x is an angle such that tan(x) = 5/12 and Pi < x < 3 Pi/2, then sec(x) =
A. 12/13
B. -12/13
C. -13/12
D. 13/12

Question 23

The real solutions to the equation cos 2(x) - 1.5 cos(x) = 1 are given by the solutions to the equation
A. cos(x) = 1
B. cos(x) = 2
C. cos(x) = 1/2
D. cos(x) = - 1/2

Question 24

Which point is on the graph of the inverse of the function f(x) = 10x + 2?
A. (100 , 0)
B. (0 , 100)
C. (10 , 0)
D. (0 , 10)

Question 25

If 10x/y = A / B, then
A. x / y = Log A / Log B
B. y = x / (Log A - Log B)
C. x = y / (Log A + Log B)
D. y = x Log (A / B)

Question 26

If Pi < x < 3 Pi/2, then sin(x) can be expressed in terms of tan(x) as follows
A. sin(x) = tan(x) / √[ 1 + tan2(x) ]
B. sin(x) = - √[ 1 + tan2(x) ] / tan(x)
C. sin(x) = - tan(x) / √[ 1 + tan2(x) ]
D. sin(x) = √[ 1 + tan2(x) ] / tan(x)

Question 27

Angle x = 11 Pi / 3 is coterminal to angle y given by
A. y = Pi / 3
B. y = Pi / 6
C. y = 5 Pi / 3
D. y = 2 Pi / 3

Question 28

If x is such that 3 Pi/2 < x < 2 Pi and sin(x) = -1 / 2, then x =
A. y = 13 Pi / 6
B. y = Pi / 3
C. y = 11 Pi / 3
D. y = 11 Pi / 6

Question 29

The exact value of cos(127 Pi/3) is given by
A. y = 1 / √(2)
B. y = 1 / 2
C. y = -1 / 2
D. y = √(3) / 2

Question 30

If Log(x - y) = 3 and Log(x + y) = 4, then x =
A. 3.5
B. 11,000
C. 5,500
D. 103.5

ANSWERS TO ABOVE QUESTIONS


1A, 2D, 3B, 4D, 5C, 6B, 7D, 8C, 9A, 10C
11A, 12B, 13A, 14B, 15D, 16B, 17D, 18C, 19B, 20D
21A, 22C, 23D, 24A, 25B, 26C, 27C, 28D, 29B, 30C

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