AP Pre-Calc Ch. 6 Review

Vectors

100

Given u = <3,-2> and v = <-1,5>, find the vector u + v

<2, 3>

200

Given a = <4,1> and b = <-2,3> find 3a - 2b

<16, -3>

300

Find the dot product of u = <5,-4> and v = <2,3>

-2

400

Find the angle between u = <3,4> and v = <5,12>

14.25 degrees

500

Find the unit vector in the opposite direction of v = <-6,8>

<3/5, -4/5>

Parametric Functions

100

Given  x(t) = 3t + 1 and y(t)=t^2-2 find the coordinates of the point where t = 3

(10,7)

200

Eliminate the parameter to write the rectangular equation in terms of x and y: 

x(t) =t-4 and y(t) = 2t+5

y = 2x + 13

300

Eliminate the parameter to write the rectangular equation and state the domain constraint for x.

x(t) = sqrtt and y(t) = 3t-1

y=3x^2 -1   

 x>=0

400

Find the AROC of y with respect to x for the parametric equations on the interval [1,3]:

x(t)=t^2 and y(t) = 3t 

3/4

500

Use Pythagorean Identity to eliminate the parameter and find the rectangular equation 

x(t) = 4 cos(t) and y(t) = 4 sin(t)

x^2+y^2= 16

Parabolas

100

Find the vertex of the parabola 

(y-3)^2=8(x+2)

(-2,3)

200

State the direction that the parabola opens

(x+4)^2= -12(y-1)

Downward

300

Find the coordinates of the focus for the parabola: 

(x-1)^2=16(y+2)

(1,2)

400

Write the standard form of the equation of a parabola with its vertex at (0,0) and a directrix of x = -5

y^2=20x

500

Complete the square to write the equation in standard form: 

y^2-4y-4x+16=0

(y-2)^2=4(x-3)

Ellipses

100

Find the center of the ellipse:

(x-5)^2/9 +(y+2)^2/25 = 1

(5,-2)

200

Find the total length of the major axis for the ellipse: 

y^2/49 +x^2/16=1

14

300

Find the distance from the center to each focus for the ellipse:

x^2/100+y^2/64 = 1

c = 6

400

Write the standard form equation of an ellipse with its center at (0,0), a horizontal major axis length of 20, and a vertical minor axis length of 10.

x^2/100 + y^2/25=1

500

Complete the square to write the ellipse equation in standard form: 

4x^2+9y^2-24x+18y+9=0

(x-3)^2/9 +(y+1)^2/4 = 1

Hyperbolas

100

Does the hyperbola open up/down or left/right? 

y^2/16 - x^2/9 = 1

Up/down (vertical transverse axis)

200

Find the center and the vertices of the hyperbola: 

(x+1)^2/25 -(y-4)^2/16 = 1

Center (-1,4) and Vertices: (4,4) and (-6,4)

300

Find the asymptotes for the hyperbola: 

y^2/36-x^2/49=1

y=+-6/7x

400

Find the coordinates of the foci for the hyperbola 

x^2/64-y^2/36=1

(10,0) and (-10,0)

500

Complete the square to write the hyperbola equation in standard form: 

9x^2-4y^2+54x+32y-19=0

(x+3)^2/4 -(y-4)^2/9 = 1