Pre-Calculus Final Exam Review

Pre-Calculus

100

What is the Law of Sines

Sin A / a = Sin B / b

200

Write the explicit rule for the sequence 2, 4, 6, 8, ...

f(n)=2(2)^n-1

300

Find the inverse function of f(x)=x²-9

f^-1(x)=sqrt(x+9)

400

Find the 5th partial sum of the geometric sequence

7, 7/3, 7/9, 7/27...

847/81

10.457

500

A flag flies 3.6 meters from the ground and casts a shadow 6.4 meters long. Find the angle of depression from the top of the flag to its shadow.

29 degrees

Final

100

State the transformations that have occurred to created the function f(x)=4x²+3 from the function g(x)=x²

Stretched vertically and shifted up 3

200

Find the direction angle of the vector <-6, 8>

126.870

300

Factor and simplify sin²x- cos²x sin²x

sin⁴x

400

Determine whether the sequence converges or diverges. If it converges give the limit

12, 4, 4/3, 4/9, ...

Converges 18

500

Find the rectangular form of the polar equation r=4/(1-cos x)

y²-8x=16

Exam

100

What is the law of cosines?

a²=b²+c²-2bcCosA

200

Find an equation of a parabola with the vertex at the origin and directrix x=-4

y²=16x

300

What value of x satisfies the equation log₂(3x+4)=3

x=4/3

400

What expression completes the Pythagorean Identity for csc²x=

1+cot²x

500

Eliminate the parameter

x=(1/4)t

y=3t²-7

y=3(4x)²-7

y=48x²-7

Review

100

Find the exact value of sin(cos^-1(0.5))

sqrt(3)/2

200

What is the range of the function h(x)=8-3(x-1)²

(-inf, 8)

300

Find 9u-3v given u=3i+4j and v=-2i+8j

33i+12j

400

Find an approximate solution 3e^2x-4=18

x=2.895

500

Find the center of the ellipse 

x²+3y²-6x-12y+16=0

(3, 2)

Yay

100

A ramp is built to a building, the ramp reaches 6 ft up and is 10 feet away from the building. How long is the ramp?

11.662 ft

200

Determine whether the sequence converges or diverges. If it converges, give the limit.

2, -4, 8, -16, ...

diverges

300

Find the magnitude of the vector <-6, 8>

10

400

Find tan(x) given csc(x) = 9/5 and x is in quadrant 2

5sqrt(56)/56

500

Find the foci of the hyperbola

(y-4)²/9 - (x+2)²/16 = 1

(-2, -1) (-2, 9)