Review of Precalculus

f (x) = 2x , g(x) = , and h(x) = x - 1 . What is f o(g o h) ?

(A)

(B) x -

(C) 2

(D) - 1

What is the end behavior of the function 3x ⁷ +2x ⁶ -3x ⁴ - x ² + x - 46 ?

What is ?

Which of the following polynomials have exactly three real roots, x = 1 , -1 , and 3 ?

What is the remainder of ?

How many possible positive and negative real roots does the function x ³ -4x ² + 3x - 2 have?

The function has what asymptotes, if any?

Which of the following expressions is not equal to the others?

(B)

(C)

(D)

The exponential rate of decay of a substance is .08 per year. What is the half-life of this substance in years?

(B) 56.5 years

(C) 8.66 years

(D) 10.035 years

Which of the following bank accounts will be worth the most in 10 years?

In which quadrants do sine and cosine have the same sign?

Which of the following is a formula for all of the quadrantal angles?

(B) θ = , where n is an integer

(D) θ = ( +1) , where n is an integer

Which of the following is not equal to the others?

(C) tan(

(D) csc

Which expression is unequal to the others?

Which of the following does not solve the equation sin(x)cos(x) = 0 ?

(A) x =

(B) x =

(C) x =

(D) x =

What is the amplitude and period of the function f (x) = 2 cos(2x) ?

(B) Amplitude: ; Period: Π

(C) Amplitude: 4 ; Period:

Which value is defined?

(C) tan()

(D) sec()

Which polar coordinates correspond to the rectangular coordinates (2, 2) ?

(A) (,)

(B) - ,

(D) (,)

Convert the polar equation 4 = r sin(θ) to rectangular form.

What are the x -intercepts, if there are any, for the function defined by x = 3t - 2 , y = t ² - 4 , -3≤t≤3 .

(A) (,)

The graph of r = 1 + 2 sin(θ) is symmetric with respect to what?

(C) The line θ =

The graph of r = 2 cos(4θ) is an example of what?

What is ı⁷7 ?

What is the polar form of z = 1 + ı ?

(A) (4,)

(B) ,)

(C) (1,)

(D) (2,)

Which of the following complex numbers has a different modulus than the rest?

(C) + ı

(D) -2ı

What are the imaginary roots of the polynomial x ⁴ +3x ³ +5x ² + 27x - 36 , if there are any?

(B) ı , - ı

What is ( + ı)⁴ ?

(C) ı - ı

Which of the following options is not a 4 th root of 1 ?

3x ² + 6x - 5y - 7 = 0 is what kind of conic?

x ² +2xy - 5y ² + 4x - 4y + 7 is what kind of conic?

Given 25x ² +4y ² - 100 = 0 , solve for a , b , and c .

(B) a = 5 , b = , c = 2

(C) a = 2 , b = 5 , c =

(D) a = 5 , b = 2 , c =

Given -4x ² +2xy - 5y ² + 6x - 2y - 1 = 0 , about how many degrees must the axes be rotated in order to eliminate the xy -term?

(A) 31.7 ^o

(B) 41.3 ^o

(C) 43.7 ^o

(D) 27.1 ^o

Given the polar equation for a conic is , what kind of conic is it?

Given is the polar form of a conic, where is the directrix in relation to the pole?

What is the next apparent term in the sequence 1, 2, 4, 5, 7, 8, 10,…

Define the sequence a _n = 3n + 6 recursively.

Define the sequence a _n = recursively.

(A) a ₁ = ; a _n+1 =

(B) a ₁ = ; a _n+1 =

(C) a ₁ = 3 ; a _n+1 =

Find an explicit formula for the following sequence: 1,, 2,, 3,, 4,… .

(A) a _n =

(C) a _n = n +

(D) a _n =

What is 7(4n - 2) ?

What is (3ⁱ) ?

Calculate the sum of the first 200 terms of a _n = n + 1 .

What is the sum of the first five terms in the sequence a _n = 2×3ⁿ ?

What is the limit of the infinite geometric series a _n = 3× ⁿ

(A)

(B)

Evaluate 5x .

(B)

(C)

Evaluate .

Calculate x ² - 4x - 2

Let f (x) = 1 for all x≠ 0 , f (x) = 4 for x = 0 . Calculate f (x) .

Over which of the following intervals is f (x) = discontinuous?

Over which of the following intervals is the function f (x) = discontinuous?

Which type of discontinuity happens to the function f (x) = at the vale x = 5 ?