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 1If f(x) = Log(x), then f^{ 1}(x) =A. 10^{ x} B. 10^{ x} C. 1 / 10^{ x} D. x^{ 10}
Question 2Log_{ 4}65 =A. 1.21 B. 1.81 C. 3.06 D. 3.01
Question 3If 2^{ 3x  1} = 16, then x =A. 3/5 B. 5/3 C. 1 D. 4
Question 4If Log_{ x}9 = 2, then x =A. 2/9 B. 9/2 C. 81 D. 3
Question 5If x^{ 2} + kx  6 = (x  2)(x + 3), then k =A. 6 B. 3 C. 1 D. 0
Question 6The vertex of the graph of y = 2x^{ 2} + 8x  3 is given byA. (8 , 3) B. (2 , 11) C. (4 , 11) D. (2 , 3)
Question 7The quadratic equation whose roots are at x = 3 and x = 5 is given byA. (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 8The roots of the equation x / (x + 2) + 3 / (x  4) = (4x + 2) / (x^{ 2}  2x  8) areA. x = 4 and x = 1 B. x = 4 only C. x = 1 only D. x = 4 only
Question 9If 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 intervalA. [0 , 9] B. [0 , 6] C. [0 , 3] D. [3 , 6]
Question 10The x intercepts of the graph of y = x^{ 2} + 3x + 18 are given byA. (6 , 3) B. (3 , 6) C. (3 , 0) and (6 , 0) D. (3 , 0) and (6 , 0)
Question 11The domain of f(x) = 2 Log x  2 is given by the intervalA. (infinity , 2) U (2 , + infinity) B. (2 , + infinity) C. (2 , + infinity) D. (infinity , + infinity)
Question 12If 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
Question 13The reference angle to angle a = 1280^{o} is equal toA. 20^{o} B. 30^{o} C. 160^{o} D. 60^{o}
Question 14If 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 15If 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 16Which 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 17Which 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 18The radian measure of an angle of 25^{o} is equal toA. 25 Pi B. 5 / (36 Pi) C. 5 Pi / 36 D. 36 / (5 Pi)
Question 19The period of the function f(x) = sin(x Pi/6 + Pi/4) is equal toA. 2 Pi B. 12 C. Pi / 6 D. 6 Pi
Question 20Which 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 21Which 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 22If 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 23The real solutions to the equation cos^{ 2}(x)  1.5 cos(x) = 1 are given by the solutions to the equationA. cos(x) = 1 B. cos(x) = 2 C. cos(x) = 1/2 D. cos(x) =  1/2
Question 24Which 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)
Question 25If 10^{x/y} = A / B, thenA. 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 26If Pi < x < 3 Pi/2, then sin(x) can be expressed in terms of tan(x) as followsA. sin(x) = tan(x) / √[ 1 + tan^{2}(x) ] B. sin(x) =  √[ 1 + tan^{2}(x) ] / tan(x) C. sin(x) =  tan(x) / √[ 1 + tan^{2}(x) ] D. sin(x) = √[ 1 + tan^{2}(x) ] / tan(x)
Question 27Angle x = 11 Pi / 3 is coterminal to angle y given byA. y = Pi / 3 B. y = Pi / 6 C. y = 5 Pi / 3 D. y = 2 Pi / 3
Question 28If 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 29The exact value of cos(127 Pi/3) is given byA. y = 1 / √(2) B. y = 1 / 2 C. y = 1 / 2 D. y = √(3) / 2
Question 30If 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 QUESTIONS1A, 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.
