1. Given the quadratic function f(x) = 2x^2+7x+3 and the linear function g(x) = x + 3, the range of the quotient function (f / g)(x) is:

a) { y R | y - 3 }

b) { y R | y 3 }

c) { y R | -5 y 5 }

d) { y R | y 4 }

e) { y R }

f) { y R | y 7 }

g) { y R | y 5 }

h) { y R | y -6 }

i) { y R | y - 5 }

j) { y R | 3 y or y -3 }

k) None of the given intervals are representing the range of the function.

2. Which statement is always false?

a) The difference of the square of tan x and the square of sec x equals two, for all real x-values.

b) The trigonometric equation csc (x) = 2 has ONLY four solutions within the interval of (0 , 4 ).

c) The origin is the only x-intercept of the curve y = 2159 (x^4) .

d) The equation of the vertical asymptote of y = - 4 / (x + 2) is x = - 2 .

e) The solution set to the absolute value inequality |1 - 3x| 2 is (- , - 1/3 ] U [ 1 , + ) .

f) cos(- 23.5) = cos (23.5).

g) 3.1415926 radian is equivalent to about 180 degrees.

3. Which one of the following rational functions has a point of discontinuity at (p , q)? (note: p and q are real numbers.)

a) y = (x - p)(x - q) / (x - p)

b) y = (x - p)(x - q) / (x - q)

c) y = (x - p)(x - p + q) / (x - p)

d) y = (x - q)(x + p - q) / (x - q)

e) None of the given functions has such point of discontinuity.

4. What are the amplitude and the magnitude of the phase shift of the following sinusoidal function y = - 3 sin (x / 4 - /12) + 9 , respectively?

a) - 3 and /12

b) 3 and /48

c) 3 and /24

d) 3 and /12

e) 3 and / 3

f) None of the given options are correct.

g) - 3 and /48

h) - 3 and /3

i) - 3 and /24

5. Since the point A(3/2 , -2) lies on the graph of y = k sin (x - /3), then the value of k must be (-4).

a) True

b) False

6. The only solutions to a trigonometric equation on the domain 0 x 2 are x = 2 / 3 and also x = 4 / 3 . An equation that has these solutions is:

a) None of the given equations has both of the given solutions.

b) 2 cos x + 1 = 0

c) 2 sin x + 1 = 0

d) 2 cos x + 3 = 0

e) 2 sin x + 3 = 0

7. If cos(A+B) = 0.8320 and cos(A-B) = 0.4358, then the decimal value of ( cos A cos B ) correct to 4 decimal places equals:

a) 1.2678

b) 0.1981

c) 0

d) 0.3962

e) 0.6339

f) 0.3626

8. The simplified form of the expression (2) [sin( / 4 + x) - sin ( / 4 - x)] is equivalent to:

a) (-2) (sin x)

b) (2) (sin x)

c) cos (x) / 2

d) - 2 cos x

e) 2 sin x

f) (- 2) (cos x)

g) - 2 sin x

h) sin (x) / 2

i) 2 cos x

j) (2) (cos x)

9. Given csc (x) = -17 / 15, where 3/2 x 2, and cot (y) = -3 / 4, where /2 y , the value of cos(x - y) equals:

a) - 4 / 85

b) 36 / 35

c) 15 / 14

d) - 84 / 85

e) 84 / 85

f) - 15 / 14

g) 14 / 15

h) - 36 / 35

i) - 14 / 15

10. The most simplified form of the trigonometric expression ( cot(x) - cot(2x) ) equals:

a) sin(2x)

b) cos(2x)

c) tan(2x)

d) sec(2x)

e) csc(2x)

f) 1

g) 1 + sin(2x)

h) 1 - sec(2x)

i) None of the given expressions are correct.

11. The remainder of the division of the quintic function f(x)=x^52x^4+ax^3x^2+bx2 by (x+1) is 7. Also, when f(x) is divided by (x2), the remainder is 32. This means that the remainder when f(x) is divided by (x1), equals:

a) -5

b) -1

c) 0

d) 2

e) 3

f) 17

g) -2

h) -3

i) 1

j) 7

12. Does the secant value of an angle whose measure is /3 radian equals 2?

a) True

b) False