__Questions 1:__

If f(x) = Log(x), then f^{ -1}(x) =

A. 10^{ x}

B. -10^{ -x}

C. 1 / 10^{ x}

D. x^{ 10}

__Questions 2:__

Log_{ 4}65 =

A. 1.21

B. 1.81

C. 3.06

D. 3.01

__Questions 3:__

If 2^{ 3x - 1} = 16, then x =

A. 3/5

B. 5/3

C. 1

D. 4

__Questions 4:__

If Log_{ x}9 = 2, then x =

A. 2/9

B. 9/2

C. 81

D. 3

__Questions 5:__

If x^{ 2} + kx - 6 = (x - 2)(x + 3), then k =

A. 6

B. 3

C. 1

D. 0

__Questions 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)

__Questions 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

__Questions 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

__Questions 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]

__Questions 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)

__Questions 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)

__Questions 12:__

If 1.56^{x} = 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

__Questions 13:__

The reference angle to angle a = -1280^{o} is equal to

A. 20^{o}

B. 30^{o}

C. 160^{o}

D. 60^{o}

__Questions 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

__Questions 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. sqrt 2

B. 1 / sqrt 2

C. - sqrt 2

D. -1 / sqrt 2

__Questions 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]

__Questions 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

__Questions 18:__

The radian measure of an angle of 25^{o} is equal to

A. 25 Pi

B. 5 / (36 Pi)

C. 5 Pi / 36

D. 36 / (5 Pi)

__Questions 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

__Questions 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)

__Questions 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

__Questions 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

__Questions 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

__Questions 24:__

Which point is on the graph of the inverse of the function f(x) = 10^{x + 2}?

A. (100 , 0)

B. (0 , 100)

C. (10 , 0)

D. (0 , 10)

__Questions 25:__

If 10^{x/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)

__Questions 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) / sqrt[ 1 + tan^{2}(x) ]

B. sin(x) = - sqrt[ 1 + tan^{2}(x) ] / tan(x)

C. sin(x) = - tan(x) / sqrt[ 1 + tan^{2}(x) ]

D. sin(x) = sqrt[ 1 + tan^{2}(x) ] / tan(x)

__Questions 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

__Questions 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

__Questions 29:__

The exact value of cos(127 Pi/3) is given by

A. y = 1 / sqrt(2)

B. y = 1 / 2

C. y = -1 / 2

D. y = sqrt(3) / 2

__Questions 30:__

If Log(x - y) = 3 and Log(x + y) = 4, then x =

A. 3.5

B. 11,000

C. 5,500

D. 10^{3.5}

**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

More math questions and problems with detailed solutions in this site.