Final Project Review of AP-Pre Calc

Conics

100

What is the equation of a circle?

(x - h)² + (y - k)² = r²

200

Identify the conic section and the center:

(x-8)²/49+(y-2)²/9=1

An ellipse with a center of (8,2).

300

What is the specific type of parabola, given the equation:

y+3=1/7(x-4)²

Vertical parabola, because the (x-4) is being squared. 

400

How do you find the p value of a parabola?

1/4p=a

500

Complete the square in order to then determine the conic section:

x²+6x+8y+1=0

(x+3)²=-8(y-1)

Parabola

Logarithmic Equations

100

What is another way you can write log₂16=4

2⁴=16

200

Solve:

4+log₄x=8

x=256

300

Solve:

log₃(8x+9)=4

x=9

400

Solve:

log₅(4x+12)=log₅(x+7)

x=-5/3

500

Solve:

log₆(3x+14)-log₆5=log₆2x

Hint: This uses one of the condensing rules.

x=2

Inverse Trig Equations

100

sin^-1(1)

π/2

200

cos^-1(tan(3π/4))

π

300

cos^-1(0)

π/2

400

arcsin(square root of 2/2)

π/4

500

cos(sin^-1(1/2))

Square root of 3/2

Content Questions

100

What is the average rate of change formula?

f(b)-f(a)/b-a

200

What is happening to the ROC if a function is concave down? Concave up?

If the function is concave down, the ROC is decreasing, and if it is concave up, the ROC is increasing.

300

3π/2 on the unit circle is equivalent to how many degrees?

270 degrees 

400

What is this equation used for?

A(t)=ae^rt

Continuous growth and decay

500

What is the domain and range of a logarithmic function?

D: (0,∞)

R: (-∞, ∞)

Trigonometry Equations/Questions

100

How do you find the period of a sine function?

Period=2π /b

200

tan (7π)

0

300

What quadrant can each inverse trig function come from?

sin^-1x

cos^-1x

tan^-1x

sin^-1x: 1 and 4

cos^-1x: 1 and 2

tan^-1x: 1 and 4

400

cot (5π/3)

Square root of -3/3

500

What are the three Pythagorean Identities?

sin²(θ) + cos²(θ) = 1

1+cot²x=csc²x

1+tan²x=sec²x