AP PreCalc Final

What is the numerical coefficient of the term containing x²y² in the expansion of (x+2y)^5?

What is the numerical coefficient of the term containing x²y² in the expansion of (x+2y)^5?

C. 40

If F(x)+x³-2x-1, the F(-2)=

C. -5

What is the domain of G(x)=square root of X-3/x²-2x?

B. All reals X≥ 3, X≠0,2

Which of the following is equivalent to the expression log∛a²b/c

C. 1/3(2loga+logb-logc)

Identify the vertical asymptote(s) for the function F(x)=x²-4/x³+2x²

D. x=0

Find the slant asymptote of f(x)= x²+2x-1/x-1

D. y=x+3

In polar coordinates, which of the following choices is not equivalent to (2,5π/6)

C. (2, -11π/6)

Given that sinx=-1/5 and tanx>0, find cosx

C. -2√6/5

Which of the following is a possible equation for the sinusoidal graph shown below? (insert graph)

D. y=2sin(π/4x)+1

Which of the following is equivalent to sin5xcos3x-cos5xsin3x?

D. sin2x

Given sinx=-1/8 and tanx<0, find sin2x

C. -3√7/32

Solve the equation log_a3-log_ab=c for b

B. 3/a^c

Given the function g(X)=-(12x-7)(34x+89), determine limx→-∞g(x)

D. ∞

Solve the inequality: 2(x-1)/(x+1)(x-3)≤0

C. (-∞,-1) u [1,3)

What is the function whose graph is a reflection over the y-axis of the graph of f(x)=1-3^x

A. g(x)=1-3^-x

Give an algebraic expression for cos(sin^-1(x))

A. √1-x²

The table shows the predicted growth of a particular bacteria after various numbers of hours. Write an explicit formula for the sequence of the number of bacteria.

D. a_n=19n

Evaluate limx→∞ 3x²-9x-4/5x²-4x+8

C. 3/5

Given the graph of the function y=f(x) shown below with points a,b,c,d,e,f,g, and h, which of the following pairs of points below has the greatest average rate of change (with graph)

D. f and h

Solve for x: 3^2x=5^x-1

A. -2.7281

Find all solutions in the interval [0,2π] for the trigonometric equation 6cos²x-5 sinx-2=0

B. π/6, 5π/6

After performing analyses on a set of data, Joseph examined the scatterplot of the residual values for each analysis. Which scatterplot indicates the best linear fit for the data? (with graphs)

C. (graph)

If cscx ≠ -1, which of the following is equivalent
cot²x/1+cscx?

B. cscx-1

If sinθ=b, then what is sinθ×cosθ×tanθ

D. b²

If f(θ)=acosθ+b, what is the minimum value of f(θ)?

A. b-a

Which of the following equations could represent the graph shown below? (graph)

B. y=-2sin(1/2x)

In the interval 0≤x<2π, what are the solutions of the equation sin²x=sinx

A. 0, π/2, π

What is the expression sin(x+π/2)/-sinx equvalent to?

C. -cotx

If sinA=3/5 and sinB=2/3 and if A and B are acute angles, what is the value of cos(A-B)?

D. (4√5+6)/15

Which of the following choices represents the graph of r=6cosθ?

B. right side circle graph

Given the polar coordinates (3, -3π/4), find the rectangular coordinates of this point

C. (-3√2/2, -3√2/2)

Given the rectangular coordinates (4, -4√3), find the polar coordinates of this point.

D. (8, 5π/3)

Let f be a function defined for all real numbers. Which of the following conditions is not sufficient to guarentee that f has an inverse function?

C. f is an even function

Which of the following functions is not odd?

C. h(x)=x⁵+1

if log_b(3^b)=b/2, then what does b equal?

D. 9

If f^-1(x) is the inverse of f(x)=2e^-x, the what does f^-1(x) equal?

A. ln(2/x)

Find f(x+h) when f(x)=2x²+4x-1

D. 2x²+4xh+2h²+4x+4h-1

Using the tables below, evaluate (f x g)(4)

C. 14

Find the horizontal asymptote, if any, for the rational function g(x)=7x²-3x-6/6-8x+3x²

B. y=7/3

If x=-2 is a real zero of the polynomial f(x)x³+12x²+46x+52, write f(x) as a product of linear factors.

C. f(x)=(x+2)(x+5+i)(x-5-i)

If θ is an angle in standard position and its terminal side passes, though the point P(-0.8,0.6) on the unit circle, which of following is a possible value radian of θ to the nearest hundreth?

B. 2.50

The height, h, in meters of a rock thrown straight up at t seconds is described by the equation h(t)=2+20t=4.9t². Find the average rate of change of the height of the rock over the first 2 seconds of flight.

D. 10.2